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This text offers an introduction to the theory of graphs and its application in engineering and science. The first part covers the main graph theoretic topics: connectivity, trees, traversability, planarity, coloring, covering, matching, digraphs, networks, matrices of a graph, graph theoretic algorithms, and matroids. In the second part, these concepts are applied to problems in engineering, operations reserach, and science as well as to an interesting set of miscellaneous problems, thus iluustrating their broad applicability. Some effort has been made to present applications that use not merely the notation and terminology of graph theory, but its actual mathematical results. Some of the applications, such as in molecular evolution, facilities layout, and graffic network design, have never appeared before in book form. Written at an advanced undergraduate to beginning graduate level, the book is suitable for students of mathematics, engineering, operations resrach, computer science, and physical sciences as well as for researchers and practitioners with an interest in graph theoretic modelling. ... Read more

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The rapidly expanding area of algebraic graph theory uses two different branches of algebra to explore various aspects of graph theory: linear algebra (for spectral theory) and group theory (for studying graph symmetry). These areas have links with other areas of mathematics, such as logic and harmonic analysis, and are increasingly being used in such areas as computer networks where symmetry is an important feature. Other books cover portions of this material, but this book is unusual in covering both of these aspects and there are no other books with such a wide scope. Peter J. Cameron, internationally recognized for his substantial contributions to the area, served as academic consultant for this volume, and the result is ten expository chapters written by acknowledged international experts in the field. Their well-written contributions have been carefully edited to enhance readability and to standardize the chapter structure, terminology and notation throughout the book. To help the reader, there is an extensive introductory chapter that covers the basic background material in graph theory, linear algebra and group theory. Each chapter concludes with an extensive list of references. ... Read more

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Substantially revised, reorganised and updated, the second edition now comprises eighteen chapters, carefully arranged in a straightforward and logical manner, with many new results and open problems.

As well as covering the theoretical aspects of the subject, with detailed proofs of many important results, the authors present a number of algorithms, and whole chapters are devoted to topics such as branchings, feedback arc and vertex sets, connectivity augmentations, sparse subdigraphs with prescribed connectivity, and also packing, covering and decompositions of digraphs. Throughout the book, there is a strong focus on applications which include quantum mechanics, bioinformatics, embedded computing, and the travelling salesman problem.

Detailed indices and topic-oriented chapters ease navigation, and more than 650 exercises, 170 figures and 150 open problems are included to help immerse the reader in all aspects of the subject.

Customer Reviews (2)

Good for experts and researchers but not for beginners
I come across this book when finding relevant materials of graph theory.As told by previous reviewer, this book contains much recent research results and is good for experts or researchers.The preface says that it is suitable for undergraduate, but in my feeling, you need to be a graduate with a full year course of graph theory completed to understand or utilize the materials of the book.The materials are presented in a standard theorem-proof format, one theorem after another.Examples are few.Though the book title contains "Algorithm", there are also few algorithms presented in the form you saw in books of computing. Probably you need to design your own algorithm after digesting the material.Besides, exercises are abundant but no hints or answers provided.

Directed graphs are more general than undirected graphs
This book reflects the main achievements of the last three decades in the directed graphs theory as well as many applications including combinatorial optimization, operations research and the fascinating area of mathematics and computer science called discrete mathematics. Since the monograph contents are given, I do not wish to go into details of material presented there.Instead I'd like to discuss the aims of the book as well as whocould be its readers.

The text strives to accomplish the following objectives:

1. To give a great deal of information on both results and prooftechniques for specialists in graph theory.No other book covers even 10\% of material provided in Digraphs,and thus before this monograph has beenpublished even specialists in graph theory very often needed tosearch for a specific result or proof techniquethrough the ocean of literature on digraphs. Now the situation has drastically improved.

2. To introduce researchers and practitioners from various otherfields in mathematics, computer science,operations research, biology, etc. to basic and more advancedresults in digraph theory and algorithms andsome carefully selected applications. It offers much more thanmerely a pure bibliography and provides theideal starting point for any researcher who needs to becomefamiliar either with theory oriented aspects ofthis interesting area or with some application in a relatively short time.

3. To provide enough material for intermediate and final year BSc or MSc courses for students in mathematics, computer science and operations research. The large number of exercises (more than 700) of various difficulty is of great help to instructors and lecturers. The applications provided in the book will help to provide enough motivation for the students to study digraph theory and algorithms.

4. To provide a large variety of topics for final year student projects in mathematics, computer science, operations research and other fields. The monograph can be used as a source for the projects because because several areas of digraph theory are covered there in real depth and they vary from relatively simple to reasonably complicated ones.

To summarize, I'd like to notice that the monograph is aimed to awide range of readers including specialists in mathematics, operations research, computer science, biology, etc.as well as students of second year and higher.

Boris Goldengorin, Department of Econometricsand Operations Research, University of Groningen, The Netherlands ... Read more

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This introductory book treats algorithmic graph theoryspecifically for programmers. It explores some key ideas and basicalgorithms in this large and rapidly growing field, and containshigh-level and language-independent descriptions of methods andalgorithms on trees, the most important type of graphs in programmingand informatics. Readers are assumed to be familiar with the basics ofgraph theory, and programming. Audience: This volume will be of interest to researchers andspecialists in programming, software engineering, data structure andinformation retrieval, and to mathematicians whose work involvesalgorithms, combinatorics, graph theory, operations research, anddiscrete optimization. The book can also be recommended as a text forgraduate courses in computer science, electronics, telecommunications,and control engineering. ... Read more

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This book will serve as a foundation for a variety of useful applications of graph theory to computer vision, pattern recognition, and related areas. It covers a representative set of novel graph-theoretic methods for complex computer vision and pattern recognition tasks. The first part of the book presents the application of graph theory to low-level processing of digital images such as a new method for partitioning a given image into a hierarchy of homogeneous areas using graph pyramids, or a study of the relationship between graph theory and digital topology. Part II presents graph-theoretic learning algorithms for high-level computer vision and pattern recognition applications, including a survey of graph based methodologies for pattern recognition and computer vision, a presentation of a series of computationally efficient algorithms for testing graph isomorphism and related graph matching tasks in pattern recognition and a new graph distance measure to be used for solving graph matching problems. Finally, Part III provides detailed descriptions of several applications of graph-based methods to real-world pattern recognition tasks. It includes a critical review of the main graph-based and structural methods for fingerprint classification, a new method to visualize time series of graphs, and potential applications in computer network monitoring and abnormal event detection.

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Sperner's theorem stimulated the development of a fast-growing theory dealing with external problems on finite sets and, more generally, on finite partially ordered sets. This book presents Sperner theory from a unified point of view, bringing combinatorial techniques together with methods from programming, linear algebra, Lie-algebra representations and eigenvalue methods, probability theory, and enumerative combinatorics. ... Read more

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In 1963 Oystein Ore wrote this classic volume, which was published in the New Mathematical Library Series. This elegant book has provided students and teachers with an excellent introduction to the field of graph theory for close to thirty years. Robin Wilson's revision adds strength to the book by updating the terminology and notation, bringing them in line with contemporary usage. Wilson has added new material on interval graphs, the traveling salesman problem, bracing frameworks, shortest route problems, and coloring maps on surfaces. Most of the diagrams in the book have been redrawn. ... Read more

Customer Reviews (1)

A Good Start on Graph Theory Applications
The book gives a good introduction for students interested in applications of graph theory. It is very clear, and guides you trough a number of very interesting examples. To give an hand on experience on graphs. There are exercise at the end of the chapter to test what you learned. The first edition is a little old and therefor the terminology is not realy up to date. ... Read more

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These four volumes contain about 9600 reviews of papers which appeared in MR between 1940 and 1978 (Volumes 1 through 56). The reviews are classified in 530 sections arranged under 27 subject headings, and appear in their entirety. In addition to an author index, both a subject index and a key index are included. ... Read more

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Participants from ten different countries attended the conference which was in many ways a sequel to a symposium held at the University of Georgia in April 1983. The principal goal of this Conference was to provide a forum for chemists and mathematicians to interact and become better informed on current activities and new developments in the broad areas of chemical topology and chemical graph theory. It is intended that this proceedings volume will make available to a wider audience a permanent record of the papers presented at the Conference. The 41 papers span a wide range of topics, and have been grouped into five major sections ... Read more

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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 of knots. The last part deals with symmetry and regularity properties. Here there are important connections with other branches of algebraic combinatorics and group theory.The structure of the volume is unchanged, but the text has been clarified and the notation brought into line with current practice. A large number of "Additional Results" are included at the end of each chapter, thereby covering most of the major advances in the past twenty years.This new and enlarged edition will be essential reading for a wide range of mathematicians, computer scientists and theoretical physicists. ... Read more

Customer Reviews (2)

Clear and (mostly) to the point
This is a very nice book, which gives an introduction to some active areas of current research, but it does not really have too much depth (even in the references), so if you are doing research in this or related subjects, I would recommendSpectra of Graphs, 87: Theory and Application (Pure and Applied Mathematics (Academic Pr)) (yes, it is out of print, and yes, it costs a mint, but your university library probably has it). Godsil's book (referered to in a previous review) is much more algebraic and much less pleasant to read than Biggs.

Well written, intriguing, but somewhat dated
I found this book very clear, concise, and well written. Most proofs seemed effortless on both the author's and reader's part. Moreover, I found the content very interesting, especially the results on the spectrum of a graph, which simply represents the eigenvalues (and their multiplicities) of the adjacency matrix (although recently it has been defined in terms of the normalized incidence matrix). It amazed me just how much mathematics can be put to bear on such a simple notion of vertices and connections between them. The only downside to this book is that algebraic graph theory has moved in many new directions since the first edition (the second edition mostly states some recent results at the end of each chapter), and the interested reader may want to supplement this book or follow up this book with the following: "Spectral Graph Theory", by Fan Chung, "Algebraic Graph Theory", by Godsil et al., and "Modern Graph Theory", by Bollobas, all of which make for graduate-level reading. And to think that some mathematics departments still show little if any desire to support fellow mathematicians who study graph theory! Reading any of these books hopefully might alter some of those entrenched attitudes. ... Read more

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Graph Theory, Combinatorics and Algorithms: Interdisciplinary Applications focuses on discrete mathematics and combinatorial algorithms interacting with real world problems in computer science, operations research, applied mathematics and engineering. The book contains eleven chapters written by experts in their respective fields, and covers a wide spectrum of high-interest problems across these discipline domains. Among the contributing authors are Richard Karp of UC Berkeley and Robert Tarjan of Princeton; both are at the pinnacle of research scholarship in Graph Theory and Combinatorics. The chapters from the contributing authors focus on "real world" applications, all of which will be of considerable interest across the areas of Operations Research, Computer Science, Applied Mathematics, and Engineering. These problems include Internet congestion control, high-speed communication networks, multi-object auctions, resource allocation, software testing, data structures, etc. In sum, this is a book focused on major, contemporary problems, written by the top research scholars in the field, using cutting-edge mathematical and computational techniques.

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The graph isomorphism problem belongs to the part of Complexity Theory that focuses on the structure of complexity classes involved in the classification of computational problems and in the relations among them. It consists in deciding whether two given graphs are isomorphic, i.e. whether there is a bijective mapping from the nodes of one graph to the nodes of the second graph such that the edge connections are respected. It is a problem of considerable practical as wen as theoretical importance that is, as of now, unresolved in the sense that no efficient algorithm for it has yet been found. Given this fact, it is natural to ask whether such an algorithm exists at an or whether the problem is intractable. -Be book focuses on this issue and presents several recent results that provide a better understanding of the relative position of the graph isomorphism problem in the class NP as well as in other complexity classes. It also uses the problem to illustrate important concepts in structural complexity, providing a look into the more general theory.'The book is basically self-contained; the only prerequisite for reading it is some elementary knowledge from Complexity Theory and Probability Theory. Its level of presentation makes it eminently suitable for a seminar or graduate course devoted to the problem, or as a rich source of examples for a standard graduate course in Complexity Theory. ... Read more

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Ramsey theory is the study of the structure of mathematical objects that is preserved under partitions. In its full generality, Ramsey theory is quite powerful, but can quickly become complicated. By limiting the focus of this book to Ramsey theory applied to the set of integers, the authors have produced a gentle, but meaningful, introduction to an important and enticing branch of modern mathematics. Ramsey Theory on the Integers offers students something quite rare for a book at this level: a glimpse into the world of mathematical research and the opportunity for them to begin pondering unsolved problems.

In addition to being the first truly accessible book on Ramsey theory, this innovative book also provides the first cohesive study of Ramsey theory on the integers. It contains perhaps the most substantial account of solved and unsolved problems in this blossoming subarea of Ramsey theory. The result is a breakthrough book that will engage students, teachers, and researchers alike. ... Read more

Customer Reviews (3)

An excellent book
An excellent book which requires only elementary mathematics to be understood and which is full of research problems

A Great Book
Great book about Ramsey theory.Clear it the exposition,good for the references,rare for the choice of research problems as well as for standard exercises.There are few books about Ramsey theory and this is,in my view, one of the best.

The Cutting Edge of Combinatorial Research for Undergrads!
This book did the impossible. It is a high-level research
monograph about a fascinating and very difficult part of
modern combinatorics, and yet accessible to (smart) undergraduate
students, who can start to do their own research right away.
It is beautifully written, in a crisp, lucid, and very engaging
style, and is also a masterpiece of historical scholarship with
ample notes. Thanks to this book we would get many more smart
students to go on to do a Ph.D. in math, students that otherwise would have gone elsewhere. We desperately need more such books. ... Read more