100 Best Graph Theory Books of All Time
We've researched and ranked the best graph theory books in the world, based on recommendations from world experts, sales data, and millions of reader ratings. Learn more
1
A stimulating excursion into pure mathematics aimed at "the mathematically traumatized," but great fun for mathematical hobbyists and serious mathematicians as well. This book leads the reader from simple graphs through planar graphs, Euler's formula, Platonic graphs, coloring, the genus of a graph, Euler walks, Hamilton walks, more. Includes exercises. 1976 edition. less
2
Written by two of the most prominent figures in the field of graph theory, this comprehensive text provides a remarkably student-friendly approach. Geared toward undergraduates taking a first course in graph theory, its sound yet accessible treatment emphasizes the history of graph theory and offers unique examples and lucid proofs. 2004 edition. less
3
Graph theory is used today in the physical sciences, social sciences, computer science, and other areas. Introductory Graph Theory presents a nontechnical introduction to this exciting field in a clear, lively, and informative style.
Author Gary Chartrand covers the important elementary topics of graph theory and its applications. In addition, he presents a large variety of proofs designed to strengthen mathematical techniques and offers challenging opportunities to have fun with mathematics.
Ten major topics — profusely illustrated — include: Mathematical Models,... more
Author Gary Chartrand covers the important elementary topics of graph theory and its applications. In addition, he presents a large variety of proofs designed to strengthen mathematical techniques and offers challenging opportunities to have fun with mathematics.
Ten major topics — profusely illustrated — include: Mathematical Models,... more
4
This outstanding introductory treatment of graph theory and its applications has had a long life in the instruction of advanced undergraduates and graduate students in all areas that require knowledge of this subject. The first nine chapters constitute an excellent overall introduction, requiring only some knowledge of set theory and matrix algebra. Topics include paths and circuits, trees and fundamental circuits, planar and dual graphs, vector and matrix representation of graphs, and related subjects.
The remaining six chapters are more advanced, covering graph theory algorithms and... more
The remaining six chapters are more advanced, covering graph theory algorithms and... more
5
In the 1980's, James Gleick's Chaos introduced the world to complexity. Now, Albert-László Barabási's Linked reveals the next major scientific leap: the study of networks. We've long suspected that we live in a small world, where everything is connected to everything else. Indeed, networks are pervasive--from the human brain to the Internet to the economy to our group of friends. These linkages, it turns out, aren't random. All networks, to the great surprise of scientists, have an underlying order and follow simple laws. Understanding the structure and behavior of these networks will help us... more
Anne-Marie SlaughterLinked is about how to understand the world in terms of networks. To understand network science the first thing to do is to visualise the world the way you visualise the Internet or even the universe – hubs of infinitely intersecting networks. As the author says, everything can be reduced to links and nodes. This book is a very accessible introduction to the science of networks and to how to... (Source)
Bill BarhydtWritten before Facebook, this book predicts what the world will look like with amazing precision. (Source)
6
This book aims to explain the basics of graph theory that are needed at an introductory level for students in computer or information sciences. To motivate students and to show that even these basic notions can be extremely useful, the book also aims to provide an introduction to the modern field of network science. Mathematics is often unnecessarily difficult for students, at times even intimidating. For this reason, explicit attention is paid in the first chapters to mathematical notations and proof techniques, emphasizing that the notations form the biggest obstacle, not the mathematical... more
7
With over 10,000 diagrams and extensive tables of properties, this atlas is comprehensive and unique. Never before has so much visual information about graphs been collected in a single volume, making it an invaluable source for researchers in graph theory, operations research and computer science.
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Science and art have in common intense seeing, the wide-eyed observing that generates visual information. Beautiful Evidence is about how seeing turns into showing, how data and evidence turn into explanation. The book identifies excellent and effective methods for showing nearly every kind of information, suggests many new designs (including sparklines), and provides analytical tools for assessing the credibility of evidence presentations (which are seen from both sides: how to produce and how to consume presentations). For alert consumers of presentations, there are chapters on... more
Recommended by Bret Victor, and 1 others. 9
The time has now come when graph theory should be part of the education of every serious student of mathematics and computer science, both for its own sake and to enhance the appreciation of mathematics as a whole. This book is an in-depth account of graph theory, written with such a student in mind; it reflects the current state of the subject and emphasizes connections with other branches of pure mathematics. The volume grew out of the author's earlier book, Graph Theory -- An Introductory Course, but its length is well over twice that of its predecessor, allowing it to reveal many exciting... more
10
Few would disagree: Life in the information age can be overwhelming. Through computers, the Internet, the media, and even our daily newspapers, we are awash in a seemingly endless stream of charts, maps, infographics, diagrams, and data. Visual Explanations is a navigational guide through this turbulent sea of information. The book is an essential reference for anyone involved in graphic, web, or multimedia design, as well as for educators and lecturers who use graphics in presentations or classes.
Jacket design: Dmitry Krasny.
Other artwork by Bonnie Scranton, Dmitry... more
Jacket design: Dmitry Krasny.
Other artwork by Bonnie Scranton, Dmitry... more
Don't have time to read the top Graph Theory books of all time? Read Shortform summaries.
Shortform summaries help you learn 10x faster by:
- Being comprehensive: you learn the most important points in the book
- Cutting out the fluff: you focus your time on what's important to know
- Interactive exercises: apply the book's ideas to your own life with our educators' guidance.
11
This is a textbook for an introductory combinatorics course lasting one or two semesters. An extensive list of problems, ranging from routine exercises to research questions, is included. In each section, there are also exercises that contain material not explicitly discussed in the preceding text, so as to provide instructors with extra choices if they want to shift the emphasis of their course.Just as with the first three editions, the new edition walks the reader through the classic parts of combinatorial enumeration and graph theory, while also discussing some recent progress in the area:... more
12
The international best-seller that makes mathematics a thrilling exploration.
In twelve dreams, Robert, a boy who hates math, meets a Number Devil, who leads him to discover the amazing world of numbers: infinite numbers, prime numbers, Fibonacci numbers, numbers that magically appear in triangles, and numbers that expand without. As we dream with him, we are taken further and further into mathematical theory, where ideas eventually take flight, until everyone - from those who fumble over fractions to those who solve complex equations in their heads - winds up marveling at what... more
In twelve dreams, Robert, a boy who hates math, meets a Number Devil, who leads him to discover the amazing world of numbers: infinite numbers, prime numbers, Fibonacci numbers, numbers that magically appear in triangles, and numbers that expand without. As we dream with him, we are taken further and further into mathematical theory, where ideas eventually take flight, until everyone - from those who fumble over fractions to those who solve complex equations in their heads - winds up marveling at what... more
13
Discover how graph algorithms can help you leverage the relationships within your data to develop more intelligent solutions and enhance your machine learning models. You'll learn how graph analytics are uniquely suited to unfold complex structures and reveal difficult-to-find patterns lurking in your data. Whether you are trying to build dynamic network models or forecast real-world behavior, this book illustrates how graph algorithms deliver value--from finding vulnerabilities and bottlenecks to detecting communities and improving machine learning predictions.
This practical book... more
This practical book... more
Recommended by Kirk Borne, and 1 others. Kirk BorneGreat book: "Graph Algorithms: Practical Examples in #ApacheSpark and @Neo4j" by @amyhodler & @markhneedham, with the Foreward by me😎 ———— Get FREE PDF copy: https://t.co/61yQgYUrud ———— #GraphAnalytics #BigData #GraphDB #LinkedData #SmartData #DataScience #AI #MachineLearning https://t.co/BQaK75O7mP (Source)
14
Addressing the prevalent issue of poorly designed quantitative information presentations, this accessible, practical, and comprehensive guide teaches how to properly create tables and graphs for effective and efficient communication. The critical numbers that measure the health, identify the opportunities, and forecast the future of organizations are often misrepresented because few people are trained to design accurate, informative materials, but this manual helps put an end to misinformation. This revised edition of the highly successful book includes updated figures and 91 additional pages... more
19
This book serves an introduction to data science, focusing on the skills and principles needed to build systems for collecting, analyzing, and interpreting data. As a discipline, data science sits at the intersection of statistics, computer science, and machine learning, but it is building a distinct heft and character of its own.
In particular, the book stresses the following basic principles as fundamental to becoming a good data scientist: "Valuing Doing the Simple Things Right," laying the groundwork of what really matters in analyzing data; "Developing Mathematical Intuition,"... more
In particular, the book stresses the following basic principles as fundamental to becoming a good data scientist: "Valuing Doing the Simple Things Right," laying the groundwork of what really matters in analyzing data; "Developing Mathematical Intuition,"... more
20
The history, formulas, and most famous puzzles of graph theory
Graph theory goes back several centuries and revolves around the study of graphs--mathematical structures showing relations between objects. With applications in biology, computer science, transportation science, and other areas, graph theory encompasses some of the most beautiful formulas in mathematics--and some of its most famous problems. The Fascinating World of Graph Theory explores the questions and puzzles that have been studied, and often solved, through graph theory. This book looks at graph... more
Graph theory goes back several centuries and revolves around the study of graphs--mathematical structures showing relations between objects. With applications in biology, computer science, transportation science, and other areas, graph theory encompasses some of the most beautiful formulas in mathematics--and some of its most famous problems. The Fascinating World of Graph Theory explores the questions and puzzles that have been studied, and often solved, through graph theory. This book looks at graph... more
Don't have time to read the top Graph Theory books of all time? Read Shortform summaries.
Shortform summaries help you learn 10x faster by:
- Being comprehensive: you learn the most important points in the book
- Cutting out the fluff: you focus your time on what's important to know
- Interactive exercises: apply the book's ideas to your own life with our educators' guidance.
21
This title is part of the Pearson Modern Classics series. Pearson Modern Classics are acclaimed titles at a value price. Please visit www.pearsonhighered.com/math-classics... for a complete list of titles.
Far more "user friendly" than the vast majority of similar books, this text is truly written with the "beginning" reader in mind. The pace is tight, the style is light, and the text emphasizes theorem proving throughout. The authors emphasize "Active Reading," a skill... more
Far more "user friendly" than the vast majority of similar books, this text is truly written with the "beginning" reader in mind. The pace is tight, the style is light, and the text emphasizes theorem proving throughout. The authors emphasize "Active Reading," a skill... more
22
With more than 200 practical recipes, this book helps you perform data analysis with R quickly and efficiently. The R language provides everything you need to do statistical work, but its structure can be difficult to master. This collection of concise, task-oriented recipes makes you productive with R immediately, with solutions ranging from basic tasks to input and output, general statistics, graphics, and linear regression.
Each recipe addresses a specific problem, with a discussion that explains the solution and offers insight into how it works. If you're a beginner, R... more
Each recipe addresses a specific problem, with a discussion that explains the solution and offers insight into how it works. If you're a beginner, R... more
23
This book fills a need for a thorough introduction to graph theory that features both the understanding and writing of proofs about graphs. Verification that algorithms work is emphasized more than their complexity. An effective use of examples, and huge number of interesting exercises, demonstrate the topics of trees and distance, matchings and factors, connectivity and paths, graph coloring, edges and cycles, and planar graphs. For those who need to learn to make coherent arguments in the fields of mathematics and computer science. less
24
Over the past decade, many major advances have been made in the field of graph colouring via the probabilistic method. This monograph provides an accessible and unified treatment of these results, using tools such as the Lovasz Local Lemma and Talagrand's concentration inequality.
The topics covered include: Kahn's proofs that the Goldberg-Seymour and List Colouring Conjectures hold asymptotically; a proof that for some absolute constant C, every graph of maximum degree Delta has a Delta+C total colouring; Johansson's proof that a triangle free graph has a O(Delta over log Delta)... more
The topics covered include: Kahn's proofs that the Goldberg-Seymour and List Colouring Conjectures hold asymptotically; a proof that for some absolute constant C, every graph of maximum degree Delta has a Delta+C total colouring; Johansson's proof that a triangle free graph has a O(Delta over log Delta)... more
25
This is a textbook on graph theory, especially suitable for computer scientists but also suitable for mathematicians with an interest in computational complexity. Although it introduces most of the classical concepts of pure and applied graph theory (spanning trees, connectivity, genus, colourability, flows in networks, matchings and traversals) and covers many of the major classical theorems, the emphasis is on algorithms and thier complexity: which graph problems have known efficient solutions and which are intractable. For the intractable problems a number of efficient approximation... more
26
These notes were first used in an introductory course team taught by the authors at Appalachian State University to advanced undergraduates and beginning graduates. The text was written with four pedagogical goals in mind: offer a variety of topics in one course, get to the main themes and tools as efficiently as possible, show the relationships between the different topics, and include recent results to convince students that mathematics is a living discipline. less
27
The primary aim of this book is to present a coherent introduction to graph theory, suitable as a textbook for advanced undergraduate and beginning graduate students in mathematics and computer science. It provides a systematic treatment of the theory of graphs without sacrificing its intuitive and aesthetic appeal. Commonly used proof techniques are described and illustrated. The book also serves as an introduction to research in graph theory. less
28
This introductory text explores the theory of graph spectra: a topic with applications across a wide range of subjects, including computer science, quantum chemistry and electrical engineering. The spectra examined here are those of the adjacency matrix, the Seidel matrix, the Laplacian, the normalized Laplacian and the signless Laplacian of a finite simple graph. The underlying theme of the book is the relation between the eigenvalues and structure of a graph. Designed as an introductory text for graduate students, or anyone using the theory of graph spectra, this self-contained treatment... more
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"Innovative introductory text . . . clear exposition of unusual and more advanced topics . . . Develops material to substantial level." — American Mathematical Monthly
"Refreshingly different . . . an ideal training ground for the mathematical process of investigation, generalization, and conjecture leading to the discovery of proofs and counterexamples." — American Mathematical Monthly
" . . . An excellent textbook for an undergraduate course." — Australian Computer Journal
A stimulating view of mathematics that appeals to students as well as teachers,... more
"Refreshingly different . . . an ideal training ground for the mathematical process of investigation, generalization, and conjecture leading to the discovery of proofs and counterexamples." — American Mathematical Monthly
" . . . An excellent textbook for an undergraduate course." — Australian Computer Journal
A stimulating view of mathematics that appeals to students as well as teachers,... more
Don't have time to read the top Graph Theory books of all time? Read Shortform summaries.
Shortform summaries help you learn 10x faster by:
- Being comprehensive: you learn the most important points in the book
- Cutting out the fluff: you focus your time on what's important to know
- Interactive exercises: apply the book's ideas to your own life with our educators' guidance.
31
With elegantly defined examples and rigorously explained theorem proofs, this book presents concepts in the theory of graphs and algorithms, and their applications. It describes many key algorithms and uses simple, clear, and logical mathematical language. less
32
Exponential random graph models (ERGMs) are increasingly applied to observed network data and are central to understanding social structure and network processes. The chapters in this edited volume provide the theoretical and methodological underpinnings of ERGMs, including models for univariate, multivariate, bipartite, longitudinal, and social-influence type ERGMs. Each method is applied in individual case studies illustrating how social science theories may be examined empirically using ERGMs. The authors supply the reader with sufficient detail to specify ERGMs, fit them to data with any... more
33
Graphs on Surfaces: Dualities, Polynomials, and Knots offers an accessible and comprehensive treatment of recent developments on generalized duals of graphs on surfaces, and their applications. The authors illustrate the interdependency between duality, medial graphs and knots; how this interdependency is reflected in algebraic invariants of graphs and knots; and how it can be exploited to solve problems in graph and knot theory. Taking a constructive approach, the authors emphasize how generalized duals and related ideas arise by localizing classical constructions, such as geometric duals... more
34
In this substantial revision of a much-quoted monograph first published in 1974, Dr. Biggs aims to express properties of graphs in algebraic terms, then to deduce theorems about them. In the first section, he tackles the applications of linear algebra and matrix theory to the study of graphs; algebraic constructions such as adjacency matrix and the incidence matrix and their applications are discussed in depth. There follows an extensive account of the theory of chromatic polynomials, a subject that has strong links with the "interaction models" studied in theoretical physics, and the theory... more
35
Too often math gets a bad rap, characterized as dry and difficult. But, Alex Bellos says, "math can be inspiring and brilliantly creative. Mathematical thought is one of the great achievements of the human race, and arguably the foundation of all human progress. The world of mathematics is a remarkable place."Bellos has traveled all around the globe and has plunged into history to uncover fascinating stories of mathematical achievement, from the breakthroughs of Euclid, the greatest mathematician of all time, to the creations of the Zen master of origami, one of the hottest areas of... more
36
The definitive book on tiling and geometric patterns, this magnificently illustrated volume features 520 figures and more than 100 tables. Accessible to anyone with a grasp of geometry, it offers numerous graphic examples of two-dimensional spaces covered with interlocking figures, in addition to related problems and references.
Suitable for geometry courses as well as independent study, this inspiring book is geared toward students, professional mathematicians, and readers interested in patterns and shapes ― artists, architects, and crystallographers, among others. Along with helpful... more
Suitable for geometry courses as well as independent study, this inspiring book is geared toward students, professional mathematicians, and readers interested in patterns and shapes ― artists, architects, and crystallographers, among others. Along with helpful... more
37
This book takes a comprehensive approach to graph theory that integrates careful exposition of classical developments with emerging methods, models, and practical needs. The authors' unparalleled treatment provides a text ideal for a two-semester course and a variety of one-semester classes, from an introductory one-semester course to courses slanted toward classical graph theory, operations research, data structures and algorithms, or algebra and topology. less
38
There has been an explosive growth in the field of combinatorial algorithms. These algorithms depend not only on results in combinatorics and especially in graph theory, but also on the development of new data structures and new techniques for analyzing algorithms. Four classical problems in network optimization are covered in detail, including a development of the data structures they use and an analysis of their running time. Data Structures and Network Algorithms attempts to provide the reader with both a practical understanding of the algorithms, described to facilitate their easy... more
40
Combining the features of a textbook with those of a problem workbook, this text for mathematics, computer science and engineering students presents a natural, friendly way to learn some of the essential ideas of graph theory. The material is explained using 360 strategically placed problems with connecting text, which is then supplemented by 280 additional homework problems. This problem-oriented format encourages active involvement by the reader while always giving clear direction. This approach is especially valuable with the presentation of proofs, which become more frequent and elaborate... more
Don't have time to read the top Graph Theory books of all time? Read Shortform summaries.
Shortform summaries help you learn 10x faster by:
- Being comprehensive: you learn the most important points in the book
- Cutting out the fluff: you focus your time on what's important to know
- Interactive exercises: apply the book's ideas to your own life with our educators' guidance.
41
1. 1 Welcome to ggplot2 ggplot2 is an R package for producing statistical, or data, graphics, but it is unlike most other graphics packages because it has a deep underlying grammar. This grammar, based on the Grammar of Graphics (Wilkinson, 2005), is composed of a set of independent components that can be composed in many di?erent ways. This makesggplot2 very powerful, because you are not limited to a set of pre-speci?ed graphics, but you can create new graphics that are precisely tailored for your problem. This may sound overwhelming, but because there is a simple set of core principles and... more
42
From the reviews: " A unique and fascinating blend, which is shown to be useful for a variety of applications, including robotics, geometrical optics, computer animation, and geometric design. The contents of the book are visualized by a wealth of carefully chosen illustrations, making the book a shear pleasure to read, or even to just browse in." Mathematical Reviews less
43
Algebraic graph theory is a combination of two strands. The first is the study of algebraic objects associated with graphs. The second is the use of tools from algebra to derive properties of graphs. The authors' goal has been to present and illustrate the main tools and ideas of algebraic graph theory, with an emphasis on current rather than classical topics. While placing a strong emphasis on concrete examples, the authors tried to keep the treatment self-contained. less
44
This revised and enlarged sixth edition of Proofs from THE BOOK features an entirely new chapter on Van der Waerden's permanent conjecture, as well as additional, highly original and delightful proofs in other chapters.
From the citation on the occasion of the 2018 "Steele Prize for Mathematical Exposition"
"... It is almost impossible to write a mathematics book that can be read and enjoyed by people of all levels and backgrounds, yet Aigner and Ziegler accomplish this feat of exposition with virtuoso style. [...] This book does an invaluable service to... more
From the citation on the occasion of the 2018 "Steele Prize for Mathematical Exposition"
"... It is almost impossible to write a mathematics book that can be read and enjoyed by people of all levels and backgrounds, yet Aigner and Ziegler accomplish this feat of exposition with virtuoso style. [...] This book does an invaluable service to... more
45
This introduction to graph theory focuses on well-established topics, covering primary techniques and including both algorithmic and theoretical problems. The algorithms are presented with a minimum of advanced data structures and programming details. This thoroughly corrected 1988 edition provides insights to computer scientists as well as advanced undergraduates and graduate students of topology, algebra, and matrix theory.
Fundamental concepts and notation and elementary properties and operations are the first subjects, followed by examinations of paths and searching, trees, and... more
Fundamental concepts and notation and elementary properties and operations are the first subjects, followed by examinations of paths and searching, trees, and... more
46
Graph Theory as I Have Known It provides a unique introduction to graph theory by one of the founding fathers, and will appeal to anyone interested in the subject. It is not intended as a comprehensive treatise, but rather as an account of those parts of the theory that have been of special interest to the author. Professor Tutte details his experience in the area, and provides a fascinating insight into how he was led to his theorems and the proofs he used. As well as being of historical interest it provides a useful starting point for research, with references to further suggested books as... more
47
In most mathematics textbooks, the most exciting part of mathematics - the process of invention and discovery - is completely hidden from the student. The aim of Knots and Surfaces is to change all that. Knots and Surfaces guides the reader through Euler's formula, one and two-sided surfaces, and knot theory using games and examples. By means of a series of carefully selected tasks, this book leads the reader on to discover some real mathematics. There are no formulas to memorize; no procedures to follow. This book is a guide to the mathematics - it starts you in the right direction and... more
48
In recent years graph theory has emerged as a subject in its own right, as well as being an important mathematical tool in such diverse subjects as operational research, chemistry, sociology and genetics. Robin Wilson's book has been widely used as a text for undergraduate courses in mathematics, computer science and economics, and as a readable introduction to the subject for non-mathematicians.
The opening chapters provide a basic foundation course, containing definitions and examples, connectedness, Eulerian and Hamiltonian paths and cycles, and trees, with a range... more
The opening chapters provide a basic foundation course, containing definitions and examples, connectedness, Eulerian and Hamiltonian paths and cycles, and trees, with a range... more
49
Confusing Textbooks? Missed Lectures? Not Enough Time?
Fortunately for you, there's Schaum's Outlines. More than 40 million students have trusted Schaum's to help them succeed in the classroom and on exams. Schaum's is the key to faster learning and higher grades in every subject. Each Outline presents all the essential course information in an easy-to-follow, topic-by-topic format. You also get hundreds of examples, solved problems, and practice exercises to test your skills.
This Schaum's Outline gives you Practice problems with full explanations that reinforce... more
Fortunately for you, there's Schaum's Outlines. More than 40 million students have trusted Schaum's to help them succeed in the classroom and on exams. Schaum's is the key to faster learning and higher grades in every subject. Each Outline presents all the essential course information in an easy-to-follow, topic-by-topic format. You also get hundreds of examples, solved problems, and practice exercises to test your skills.
This Schaum's Outline gives you Practice problems with full explanations that reinforce... more
50
The ever-expanding field of extremal graph theory encompasses a diverse array of problem-solving methods, including applications to economics, computer science, and optimization theory. This volume, based on a series of lectures delivered to graduate students at the University of Cambridge, presents a concise yet comprehensive treatment of extremal graph theory.
Unlike most graph theory treatises, this text features complete proofs for almost all of its results. Further insights into theory are provided by the numerous exercises of varying degrees of difficulty that accompany each... more
Unlike most graph theory treatises, this text features complete proofs for almost all of its results. Further insights into theory are provided by the numerous exercises of varying degrees of difficulty that accompany each... more
Don't have time to read the top Graph Theory books of all time? Read Shortform summaries.
Shortform summaries help you learn 10x faster by:
- Being comprehensive: you learn the most important points in the book
- Cutting out the fluff: you focus your time on what's important to know
- Interactive exercises: apply the book's ideas to your own life with our educators' guidance.
51
Starting from dimensional analysis and physical similarity, G. Barenblatt describes the art of discovering scaling laws. He demonstrates the concepts of intermediate asymptotics and the renormalization group as natural consequences of self-similarity and shows how and when these tools can tackle the task at hand, and when they cannot. Based on courses taught to undergraduate and graduate students, the book can also be used independently by biologists, chemists, astronomers, engineers and geoscientists. less
52
Additive combinatorics is the theory of counting additive structures in sets. This theory has seen exciting developments and dramatic changes in direction in recent years thanks to its connections with areas such as number theory, ergodic theory and graph theory. This graduate-level 2006 text will allow students and researchers easy entry into this fascinating field. Here, the authors bring together in a self-contained and systematic manner the many different tools and ideas that are used in the modern theory, presenting them in an accessible, coherent, and intuitively clear manner, and... more
53
Graphs drawn on two-dimensional surfaces have always attracted researchers by their beauty and by the variety of difficult questions to which they give rise. The theory of such embedded graphs, which long seemed rather isolated, has witnessed the appearance of entirely unexpected new applications in recent decades, ranging from Galois theory to quantum gravity models, and has become a kind of a focus of a vast field of research. The book provides an accessible introduction to this new domain, including such topics as coverings of Riemann surfaces, the Galois group action on embedded graphs... more
54
Recently, a variety ofresults on the complexitystatusofthegraph isomorphism problem has been obtained. These results belong to the so-called structural part of Complexity Theory. Our idea behind this book is to summarize such results which might otherwise not be easily accessible in the literature, and also, to give the reader an understanding of the aims and topics in Structural Complexity Theory, in general. The text is basically self contained; the only prerequisite for reading it is some elementary knowledge from Complexity Theory and Probability Theory. It can be used to teach a seminar... more
55
This is an advanced text and research monograph on groups acting on low-dimensional toplogical spaces, and for the most part the viewpoint is algebraic. Much of the book occurs at the one-dimensional level, where the topology becomes graph theory. Here the treatment includes several of the standard results on groups acting on trees, as well as many original results on ends of groups and Boolean rings of graphs. Two-dimensional topics include the characterization of Poincare duality groups and accessibility of almost finitely presented groups. The main Three-dimensional topics are the... more
56
Provides the first comprehensive treatment of theoretical, algorithmic, and application aspects of domination in graphs-discussing fundamental results and major research accomplishments in an easy-to-understand style. Includes chapters on domination algorithms and NP-completeness as well as frameworks for domination. less
58
The primary intent of the book is to introduce an array of beautiful problems in a variety of subjects quickly, pithily and completely rigorously to graduate students and advanced undergraduates. The book takes a number of specific problems and solves them, the needed tools developed along the way in the context of the particular problems. It treats a melange of topics from combinatorial probability theory, number theory, random graph theory and combinatorics. The problems in this book involve the asymptotic analysis of a discrete construct as some natural parameter of the system tends to... more
59
Beginning with the origin of the four color problem in 1852, the field of graph colorings has developed into one of the most popular areas of graph theory. Introducing graph theory with a coloring theme, Chromatic Graph Theory explores connections between major topics in graph theory and graph colorings as well as emerging topics.
This self-contained book first presents various fundamentals of graph theory that lie outside of graph colorings, including basic terminology and results, trees and connectivity, Eulerian and Hamiltonian graphs, matchings and... more
This self-contained book first presents various fundamentals of graph theory that lie outside of graph colorings, including basic terminology and results, trees and connectivity, Eulerian and Hamiltonian graphs, matchings and... more
60
The leading reference on probabilistic methods in combinatorics-now expanded and updated
When it was first published in 1991, The Probabilistic Method became instantly the standard reference on one of the most powerful and widely used tools in combinatorics. Still without competition nearly a decade later, this new edition brings you up to speed on recent developments, while adding useful exercises and over 30% new material. It continues to emphasize the basic elements of the methodology, discussing in a remarkably clear and informal style both algorithmic and classical methods as... more
When it was first published in 1991, The Probabilistic Method became instantly the standard reference on one of the most powerful and widely used tools in combinatorics. Still without competition nearly a decade later, this new edition brings you up to speed on recent developments, while adding useful exercises and over 30% new material. It continues to emphasize the basic elements of the methodology, discussing in a remarkably clear and informal style both algorithmic and classical methods as... more
Don't have time to read the top Graph Theory books of all time? Read Shortform summaries.
Shortform summaries help you learn 10x faster by:
- Being comprehensive: you learn the most important points in the book
- Cutting out the fluff: you focus your time on what's important to know
- Interactive exercises: apply the book's ideas to your own life with our educators' guidance.
61
Counting: The Art of Enumerative Combinatorics provides an introduction to discrete mathematics that addresses questions that begin, How many ways are there to...For example, �How many ways are there to order a collection of 12 ice cream cones if 8 flavors are available?� At the end of the book the reader should be able to answer such nontrivial counting questions as, �How many ways are there to color the faces of a cube if �k� colors are available with each face having exactly one color?� or �How many ways are there to stack �n� poker chips, each of which can be red, white, blue, or green,... more
62
Behind the familiar surfaces of the telephone, radio, and television lies a sophisticated and intriguing body of knowledge known as information theory. This is the theory that has permitted the rapid development of all sorts of communication, from color television to the clear transmission of photographs from the vicinity of Jupiter.
To give a solid introduction to this burgeoning field, J. R. Pierce has revised his well-received 1961 study of information theory for a second edition. Beginning with the origins of the field, Dr. Pierce follows the brilliant formulations of Claude... more
To give a solid introduction to this burgeoning field, J. R. Pierce has revised his well-received 1961 study of information theory for a second edition. Beginning with the origins of the field, Dr. Pierce follows the brilliant formulations of Claude... more
64
This introduction to some of the principal models in the theory of disordered systems leads the reader through the basics, to the very edge of contemporary research, with the minimum of technical fuss. Topics covered include random walk, percolation, self-avoiding walk, interacting particle systems, uniform spanning tree, random graphs, as well as the Ising, Potts, and random-cluster models for ferromagnetism, and the Lorentz model for motion in a random medium. Schramm-Lowner evolutions (SLE) arise in various contexts. The choice of topics is strongly motivated by modern applications and... more
65
A comprehensive introduction to network flows that brings together the classic and the contemporary aspects of the field, and provides an integrative view of theory, algorithms, and applications.
presents in-depth, self-contained treatments of shortest path, maximum flow, and minimum cost flow problems, including descriptions of polynomial-time algorithms for these core models. emphasizes powerful algorithmic strategies and analysis tools such as data scaling, geometric improvement arguments, and potential function arguments. provides an easy-to-understand descriptions of several... more
presents in-depth, self-contained treatments of shortest path, maximum flow, and minimum cost flow problems, including descriptions of polynomial-time algorithms for these core models. emphasizes powerful algorithmic strategies and analysis tools such as data scaling, geometric improvement arguments, and potential function arguments. provides an easy-to-understand descriptions of several... more
66
This is a new edition of the now classic text. The already extensive treatment given in the first edition has been heavily revised by the author. The addition of two new sections, numerous new results and 150 references means that this represents an up-to-date and comprehensive account of random graph theory. The theory estimates the number of graphs of a given degree that exhibit certain properties. It not only has numerous combinatorial applications, but also serves as a model for the probabilistic treatment of more complicated random structures. This book, written by an acknowledged expert... more
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Abacus Mind Math Level 1 - Workboook 1 of 2 (for students):
This is a Workbook. It contains only practice work for children/adults who are trying to learn soroban. Instructions on how to use this workbook, how to learn soroban, and how to teach children soroban are all covered in the Instruction book which is sold seperately under the title: Abacus Mind Math Instruction Book Level 1: Step by Step Guide to Excel at Mind Math with Soroban, a Japanese Abacus.
Level 1 has three books; one Instruction book and two Workbooks. The Instruction book... more
This is a Workbook. It contains only practice work for children/adults who are trying to learn soroban. Instructions on how to use this workbook, how to learn soroban, and how to teach children soroban are all covered in the Instruction book which is sold seperately under the title: Abacus Mind Math Instruction Book Level 1: Step by Step Guide to Excel at Mind Math with Soroban, a Japanese Abacus.
Level 1 has three books; one Instruction book and two Workbooks. The Instruction book... more
68
The application of graph theory to modelling systems began in several scientific areas, among them statistical physics (the study of large particle systems), genetics (studying inheritable properties of natural species), and interactions in contingency tables. The use of graphical models in statistics has increased considerably in these and other areas such as artificial intelligence, and the theory has been greatly developed and extended. This is the first comprehensive and authoritative account of the theory of graphical models. Written by a leading expert in the field, it contains the... more
69
A brand new, fully updated edition of the most widely-used, frequently-cited, and critically acclaimed multicultural text in the mental health field
This fully revised, 8th edition of the market-leading textbook on multicultural counseling comprehensively covers the most recent research and theoretical formulations that introduce and analyze emerging important multicultural topical developments. It examines the concept of "cultural humility" as part of the major characteristics of cultural competence in counselor education and practice; roles of white allies in multicultural... more
This fully revised, 8th edition of the market-leading textbook on multicultural counseling comprehensively covers the most recent research and theoretical formulations that introduce and analyze emerging important multicultural topical developments. It examines the concept of "cultural humility" as part of the major characteristics of cultural competence in counselor education and practice; roles of white allies in multicultural... more
70
There are many distinct pleasures associated with computer programming. Craftsm- ship has its quiet rewards, the satisfaction that comes from building a useful object and making it work. Excitement arrives with the ?ash of insight that cracks a previously intractable problem. The spiritual quest for elegance can turn the hacker into an artist. Therearepleasuresinparsimony, insqueezingthelastdropofperformanceoutofclever algorithms and tight coding. Thegames, puzzles, andchallengesofproblemsfrominternationalprogrammingc-... more
Don't have time to read the top Graph Theory books of all time? Read Shortform summaries.
Shortform summaries help you learn 10x faster by:
- Being comprehensive: you learn the most important points in the book
- Cutting out the fluff: you focus your time on what's important to know
- Interactive exercises: apply the book's ideas to your own life with our educators' guidance.
71
Preface to First Edition Before writing the graphics for SYSTAT in the 1980's, I began by teaching a seminar in statistical graphics and collecting as many different quantitative graphics as I could find. I was determined to produce a package that could draw every statistical graphic I had ever seen. The structure of the program was a collection of procedures named after the basic graph types they p- duced. The graphics code was roughly one and a half megabytes in size. In the early 1990's, I redesigned the SYSTAT graphics package using - ject-based technology. I intended to produce a more... more
72
Abacus Mind Math Instruction Book Level 1 (for teachers and parents):
Goal for Level - 1 Addition - without carryover problems Subtraction - without borrowing problems Topics covered: Basics of abacus How to do mind math How to do dictation 5 exchange concepts explained in detail with examples Skill building activities explained
Instruction book includes:
Examples for each concept with detailed pictures and steps by step instruction on how to calculate and what to tell your students while teaching. Theory behind the formulas explained in simple terms. Over 380 sample... more
Goal for Level - 1 Addition - without carryover problems Subtraction - without borrowing problems Topics covered: Basics of abacus How to do mind math How to do dictation 5 exchange concepts explained in detail with examples Skill building activities explained
Instruction book includes:
Examples for each concept with detailed pictures and steps by step instruction on how to calculate and what to tell your students while teaching. Theory behind the formulas explained in simple terms. Over 380 sample... more
73
Clear, comprehensive introduction emphasizes graph imbedding but also covers thoroughly the connections between topological graph theory and other areas of mathematics. Discussion of imbeddings into surfaces is combined with a complete proof of the classification of closed surfaces. Authors explore the role of voltage graphs in the derivation of genus formulas, explain the Ringel-Youngs theorem — a proof that revolutionized the field of graph theory — and examine the genus of a group, including imbeddings of Cayley graphs. 1987 edition. Many figures. less
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NOTE: Originally designed as a paperback book, the digital edition is designed to work with pinch-and-zoom. Also, whereas the paperback provides room to draw graphs or work out solutions, the digital edition requires graph paper and scratch paper for drawing or working out solutions. The answers to the exercises are tabulated at the back, which can be accessed via device navigation.
WHAT TO EXPECT: Learn basic coordinate algebra graphing skills with this practice workbook: basic graphing terminology reading (x, y) coordinates signs in... more
WHAT TO EXPECT: Learn basic coordinate algebra graphing skills with this practice workbook: basic graphing terminology reading (x, y) coordinates signs in... more
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Based on 10 lectures given at the CBMS workshop on spectral graph theory in June 1994 at Fresno State University, this exposition can be likened to a conversation with a good teacher - one who not only gives you the facts, but tells you what is really going on, why it is worth doing, and how it is related to familiar ideas in other areas. less
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This volume explores the various ways in which integer-valued graph theory concepts can be modified to derive nonintegral values. It explains the general theory of hypergraphs and presents in-depth coverage of fundamental and advanced topics, including fractional matching, fractional coloring, fractional edge coloring, fractional arboricity via matroid methods, fractional isomorphism, and additional subjects. 1997 edition. less
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From specialists in the field, you will learn about interesting connections and recent developments in the field of graph theory by looking in particular at Cartesian products-arguably the most important of the four standard graph products. Many new results in this area appear for the first time in print in this book. Written in an accessible way, this book can be used for personal study in advanced applications of graph theory or for an advanced graph theory course. less
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Abacus Mind Math Level 1 - Workbook 2 (for students):
Topics covered:
Dictation
Plus and minus 2, 3, and 4 of 5 exchange concepts
Workbook 2 includes over 1575 practice problems for children to learn and master concepts introduced.
Use this practice Workbook - 2 after completing:
Abacus Mind Math Level 1 Workbook 1: Excel at Mind Math with Soroban, a Japanese Abacus
Corresponding instruction for teachers and parents is sold separately under the title:
Abacus Mind Math Instruction Book Level... more
Topics covered:
Dictation
Plus and minus 2, 3, and 4 of 5 exchange concepts
Workbook 2 includes over 1575 practice problems for children to learn and master concepts introduced.
Use this practice Workbook - 2 after completing:
Abacus Mind Math Level 1 Workbook 1: Excel at Mind Math with Soroban, a Japanese Abacus
Corresponding instruction for teachers and parents is sold separately under the title:
Abacus Mind Math Instruction Book Level... more
80
Confusing Textbooks?
Missed Lectures?
Tough Test Questions?
Fortunately for you, there's Schaum's Outlines. More than 40 million students have trusted Schaum's to help them succeed in the classroom and on exams. Schaum's is the key to faster learning and higher grades in every subject. Each Outline presents all the essential course information in an easy-to-follow, topic-by-topic format. You also get hundreds of examples, solved problems, and practice exercises to test your skills.
This Schaum's Outline gives you more
Missed Lectures?
Tough Test Questions?
Fortunately for you, there's Schaum's Outlines. More than 40 million students have trusted Schaum's to help them succeed in the classroom and on exams. Schaum's is the key to faster learning and higher grades in every subject. Each Outline presents all the essential course information in an easy-to-follow, topic-by-topic format. You also get hundreds of examples, solved problems, and practice exercises to test your skills.
This Schaum's Outline gives you more
Don't have time to read the top Graph Theory books of all time? Read Shortform summaries.
Shortform summaries help you learn 10x faster by:
- Being comprehensive: you learn the most important points in the book
- Cutting out the fluff: you focus your time on what's important to know
- Interactive exercises: apply the book's ideas to your own life with our educators' guidance.
81
The Turin Shroud is the most important and studied relic in the world. Many papers on it have recently appeared in important scientific journals. Scientific studies on the relic until today have failed to provide conclusive answers about the identity of the enveloped man and the dynamics regarding the image formation impressed therein. This book not only addresses these issues in a scientific and objective manner but also leads the reader through new search paths. It summarizes the results in a simple manner for the reader to comprehend easily. Many books on the theme have been already... more
82
Discover how graph databases can help you manage and query highly connected data. With this practical book, you’ll learn how to design and implement a graph database that brings the power of graphs to bear on a broad range of problem domains. Whether you want to speed up your response to user queries or build a database that can adapt as your business evolves, this book shows you how to apply the schema-free graph model to real-world problems.
Learn how different organizations are using graph databases to outperform their competitors. With this book’s data modeling, query, and code... more
Learn how different organizations are using graph databases to outperform their competitors. With this book’s data modeling, query, and code... more
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Complex interacting networks are observed in systems from such diverse areas as physics, biology, economics, ecology, and computer science. For example, economic or social interactions often organize themselves in complex network structures. Similar phenomena are observed in traffic flow and in communication networks as the internet. In current problems of the Biosciences, prominent examples are protein networks in the living cell, as well as molecular networks in the genome. On larger scales one finds networks of cells as in neural networks, up to the scale of organisms in ecological food... more
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Contains a wealth of information previously scattered in research journals, conference proceedings and technical reports. Identifies more than 200 unsolved problems. Every problem is stated in a self-contained, extremely accessible format, followed by comments on its history, related results and literature. The book will stimulate research and help avoid efforts on solving already settled problems. Each chapter concludes with a comprehensive list of references which will lead readers to original sources, important contributions and other surveys. less
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The second in a series of systematic studies by a celebrated mathematician I. M. Gelfand and colleagues, this volume presents students with a well-illustrated sequence of problems and exercises designed to illuminate the properties of functions and graphs. Since readers do not have the benefit of a blackboard on which a teacher constructs a graph, the authors abandoned the customary use of diagrams in which only the final form of the graph appears; instead, the book's margins feature step-by-step diagrams for the complete construction of each graph. The first part of the book employs simple... more
86
Starting around the late 1950s, several research communities began relating the geometry of graphs to stochastic processes on these graphs. This book, twenty years in the making, ties together research in the field, encompassing work on percolation, isoperimetric inequalities, eigenvalues, transition probabilities, and random walks. Written by two leading researchers, the text emphasizes intuition, while giving complete proofs and more than 850 exercises. Many recent developments, in which the authors have played a leading role, are discussed, including percolation on trees and Cayley graphs,... more
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The first part of this text covers the main graph theoretic topics: connectivity, trees, traversability, planarity, colouring, covering, matching, digraphs, networks, matrices of a graph, graph theoretic algorithms, and matroids. These concepts are then applied in the second part to problems in engineering, operations research, and science as well as to an interesting set of miscellaneous problems, thus illustrating their broad applicability. Every effort has been made to present applications that use not merely the notation and terminology of graph theory, but also its actual mathematical... more
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Introduction to Probability Models, Ninth Edition, is the primary text for a first undergraduate course in applied probability. This updated edition of Ross's classic bestseller provides an introduction to elementary probability theory and stochastic processes, and shows how probability theory can be applied to the study of phenomena in fields such as engineering, computer science, management science, the physical and social sciences, and operations research. With the addition of several new sections relating to actuaries, this text is highly recommended by the Society of... more
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Don't have time to read the top Graph Theory books of all time? Read Shortform summaries.
Shortform summaries help you learn 10x faster by:
- Being comprehensive: you learn the most important points in the book
- Cutting out the fluff: you focus your time on what's important to know
- Interactive exercises: apply the book's ideas to your own life with our educators' guidance.
91
This undergraduate textbook provides an introduction to graph theory, which has numerous applications in modeling problems in science and technology, and has become a vital component to computer science, engineering, and mathematics curricula of universities all over the world.
The author follows a methodical and easy to understand approach. Beginning with the historical background, motivation and applications of graph theory, the author first explains basic graph theoretic terminologies. From this firm foundation, the author goes on to present paths, cycles, connectivity, trees,... more
The author follows a methodical and easy to understand approach. Beginning with the historical background, motivation and applications of graph theory, the author first explains basic graph theoretic terminologies. From this firm foundation, the author goes on to present paths, cycles, connectivity, trees,... more
92
From reviews of the previous editions .... The book is a first class textbook and seems to be indispensable for everybody who has to teach combinatorial optimization. It is very helpful for students, teachers, and researchers in this area. The author finds a striking synthesis of nice and interesting mathematical results and practical applications. ... the author pays much attention to the inclusion of well-chosen exercises. The reader does not remain helpless; solutions or at least hints are given in the appendix. Except for some small basic mathematical and algorithmic knowledge the book is... more
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Once considered an "unimportant" branch of topology, graph theory has come into its own through many important contributions to a wide range of fields - and is now one of the fastest-growing areas in discrete mathematics and computer science. This practical, intuitive book introduces basic concepts, definitions, theorems, and examples from graph theory. KEY TOPICS: Presents a collection of interesting results from mathematics that involve key concepts and proof techniques. Covers design and analysis of computer algorithms for solving problems in graph theory. Discusses... more
95
William Playfair is best known as an ingenious Scot of questionable repute who happened to invent "statistical graphics"--the line, bar, and pie charts we use today. Some are also aware he developed theories explaining international trade and investment, made contributions to concepts like price indexes and measures of national power, and pioneered strategic analysis.
Yet even those familiar with his work will be surprised to learn that Playfair was, in fact, a secret agent, carrying out espionage and subversion against France on behalf of Great Britain. Many of his contributions... more
Yet even those familiar with his work will be surprised to learn that Playfair was, in fact, a secret agent, carrying out espionage and subversion against France on behalf of Great Britain. Many of his contributions... more
96
MATLAB(R), now the industry-standard engineering language for computation, analysis, and visualization, continues to evolve in its capabilities. Version 6.x incorporated several major improvements, including significant enhancements to its graphics features, such as transparencies, increased 3-D visualization, and an improved rendering engine.
The bestselling Graphics and GUIs with MATLAB has been fully revised to reflect MATLAB version 6. The third edition also features a number of improvements in both content and organization that ensure its readers get the optimum level of... more
The bestselling Graphics and GUIs with MATLAB has been fully revised to reflect MATLAB version 6. The third edition also features a number of improvements in both content and organization that ensure its readers get the optimum level of... more
97
Graphs & Digraphs masterfully employs student-friendly exposition, clear proofs, abundant examples, and numerous exercises to provide an essential understanding of the concepts, theorems, history, and applications of graph theory.
Fully updated and thoughtfully reorganized to make reading and locating material easier for instructors and students, the Sixth Edition of this bestselling, classroom-tested text:
Adds more than 160 new exercises
Presents many new concepts, theorems, and examples
... more
98
Sometimes, when you’re stumped for a solution to a problem, the best thing to do is to relax. Free your mind. Doodle. Whether you’re a budding Picasso or a novice artist, your drawings and scribbles can help you learn even the most difficult concepts. You can doodle yourself smart!
With Doodle Yourself Smart...Math, you can learn about patterns, prime numbers, and more of math’s most fascinating aspects. This fun and educational book includes more than 100 doodles and problems covering key concepts and ideas. There’s plenty of space for scribbling solutions--but there’s also... more
With Doodle Yourself Smart...Math, you can learn about patterns, prime numbers, and more of math’s most fascinating aspects. This fun and educational book includes more than 100 doodles and problems covering key concepts and ideas. There’s plenty of space for scribbling solutions--but there’s also... more
99
Graph algorithms is a well-established subject in mathematics and computer science. Beyond classical application fields, like approximation, combinatorial optimization, graphics, and operations research, graph algorithms have recently attracted increased attention from computational molecular biology and computational chemistry. Centered around the fundamental issue of graph isomorphism, this text goes beyond classical graph problems of shortest paths, spanning trees, flows in networks, and matchings in bipartite graphs. Advanced algorithmic results and techniques of practical relevance are... more
Don't have time to read the top Graph Theory books of all time? Read Shortform summaries.
Shortform summaries help you learn 10x faster by:
- Being comprehensive: you learn the most important points in the book
- Cutting out the fluff: you focus your time on what's important to know
- Interactive exercises: apply the book's ideas to your own life with our educators' guidance.