Book Description

Customer Reviews (2)

A recognized Classical text
This book had much that I needed to know about graph theory.
It is well written and includes much of the information needed.

It has three problems in notation that bother me:
1) Bn for Bouquets is like the Bn used for Braid groups.
2) definitions of "stars" are more the classical star than
the current usage as central point with radial connections.
3)The book doesn't distinguish well enough
between "graphs" with are symmetrical adjacency matrices
and "digraphs" and ends up confusing the issue it should clarify.

The book also shorts the reader on matrix theory connected to the graphs.
It tends to use an older approach to graphs that has to be adapted to modern computer mathematical systems.

Excellent
This book is written at a graduate level.It is written, for the most part, clearly and methodically.There are about 300 problems throughout the text, but there are no solutions in this book for those problems.

Titles of the 6 Chapters (with the number of pages in each chapter): 1) Introduction (to graph theory), 55; 2) Voltage Graphs and Covering Spaces, 40; 3) Surfaces and Graph Embeddings, 68; 4) Imbedded Voltage Graphs and Current Graphs, 54; 5) Map Colorings, 35; and 6) The Genus of a Group, 71.

This book is sufficient for self-study. ... Read more

Book Description
Written by one of the leading authors in the field, this text provides a student-friendly approach to graph theory for undergraduates.Much care has been given to present the material at the most effective level for students taking a first course in graph theory.Gary Chartrand and Ping Zhang's lively and engaging style, historical emphasis, unique examples and clearly-written proof techniques make it a sound yet accessible text that stimulates interest in an evolving subject and exploration in its many applications.

This text is part of the Walter Rudin Student Series in Advanced Mathematics. ... Read more

Customer Reviews (1)

An excellent text
This textbook was such a great complement to the course I took in Graph Theory.Everything is explained beautifully, from simple things such as definitions of elementary terms to subjects more complex such as the coloring theorems of Vizing and Shannon.Proofs accompany nearly all theorems/conjectures in the book, and they are done in a clear and concise manner.What I also found particularly interesting were the various historical pieces that the authors added to the book.They are not only interesting but they serve as a nice break between sections of purely technical content.

This is a great text to have on hand for an introductory course and I highly recommend it for anyone looking for such a text. ... Read more

Book Description
Graph theory is an important branch of contemporary combinatorial mathematics.By describing recent results in algebraic graph theory and demonstrating how linear algebra can be used to tackle graph-theoretical problems, the authors provide new techniques for specialists in graph theory. The book explains how the spectral theory of finite graphs can be strengthened by exploiting properties of the eigenspaces of adjacency matrices associated with a graph. The extension of spectral techniques proceeds at three levels: using eigenvectors associated with an arbitrary labeling of graph vertices, using geometrical invariants of eigenspaces such as graph angles and main angles, and introducing certain kinds of canonical eigenvectors by means of star partitions and star bases.Current research on these topics is part of a wider effort to forge closer links between algebra and combinatorics. Problems of graph reconstruction and identification are used to illustrate the importance of graph angles and star partitions in relation to graph structure. Specialists in graph theory will welcome this treatment of important new research. ... Read more

Book Description
Algebraic graph theory is a fascinating subject concerned with the interplay between algebra and graph theory.Algebraic tools can be used to give surprising and elegant proofs of graph theoretic facts, and there are many interesting algebraic objects associated with graphs.The authors take an inclusive view of the subject, and present a wide range of topics.These range from standard classics, such as the characterization of line graphs by eigenvalues, to more unusual areas such as geometric embeddings of graphs and the study of graph homomorphisms.The authors' goal has been to present each topic in a self-contained fashion, presenting the main tools and ideas, with an emphasis on their use in understanding concrete examples.A substantial proportion of the book covers topics that have not appeared in book form before, and as such it provides an accessible introduction to the research literature and to important open questions in modern algebraic graph theory.This book is primarily aimed at graduate students and researchers in graph theory, combinatorics, or discrete mathematics in general. However, all the necessary graph theory is developed from scratch, so the only pre-requisite for reading it is a first course in linear algebra and a small amount of elementary group theory.It should be accessible to motivated upper-level undergraduates.Chris Godsil is a full professor in the Department of Combinatorics andOptimization at the University of Waterloo. His main research interests lie in the interactions between algebra and combinatorics, in particular the application of algebraic techniques to graphs, designs and codes. He has published more than 70 papers in these areas, is a founding editor of "The Journal of Algebraic Combinatorics" and is the author of the book "Algebraic Combinatorics".Gordon Royle teaches in the Department of Computer Science & Software Engineering at the University of Western Australia.His main research interests lie in the application of computers to combinatorial problems, in particular the cataloguing, enumeration and investigation of graphs, designs and finite geometries. He has published more than 30 papers in graph theory, design theory and finite geometry. ... Read more

Customer Reviews (1)

an introduction to an interesting subject
--The first part of the book is devoted to quite hard chapters on transitive, arc-transitive graph,homomorphism, etc.

--The second part is about Matrix theory, interlacing, strongly regular graph, two graph, generalized line graph, etc it is the main part of the book.

--The third part is about cut, flows, Knots, etc.

This book can serve as a nice introduction to thesubject of Graph theory.

Nevertheless:

--This book lacks some more example, for this see "distance regular graph".

--It is sketchy on chromatic polynomial, planar graph.

--The original book by Norman Biggs is shorter, smarter, nicer ... Read more

Book Description
With examples of all 450 functions in action plus tutorial text on the mathematics, this book is the definitive guide to Experimenting with Combinatorica, a widely used software package for teaching and research in discrete mathematics. Three interesting classes of exercises are provided--theorem/proof, programming exercises, and experimental explorations--ensuring great flexibility in teaching and learning the material.The Combinatorica user community ranges from students to engineers, researchers in mathematics, computer science, physics, economics, and the humanities. Recipient of the EDUCOM Higher Education Software Award, Combinatorica is included with every copy of the popular computer algebra system Mathematica. ... Read more

Book Description
The four-colour theorem is one of the famous problems of mathematics, that frustrated generations of mathematicians from its birth in 1852 to its solution (using substantial assistance from electronic computers) in 1976. The theorem asks whether four colours are sufficient to colour all conceivable maps, in such a way that countries with a common border are coloured with different colours.The book discusses various attempts to solve this problem, and some of the mathematics which developed out of these attempts. Much of this mathematics has developed a life of its own, and forms a fascinating part of the subject now known as graph theory.The book is designed to be self-contained, and develops all the graph-theoretical tools needed as it goes along. It includes all the elementary graph theory that should be included in an introduction to the subject, before concentrating on specific topics relevant to the four-colour problem.Part I covers basic graph theory, Euler's polyhedral formula, and the first published false `proof' of the four-colour theorem. Part II ranges widely through related topics, including map-colouring on surfaces with holes, the famous theorems of Kuratowski, Vizing, and Brooks, the conjectures of Hadwiger and Hajos, and much more besides. In Part III we return to the four-colour theorem, and study in detail the methods which finally cracked the problem. ... Read more

Book Description
Discrete Mathematics is one of the fastest growing areas in mathematics today with an ever-increasing number of courses in schools and universities. Graphs and Applications is based on a highly successful Open University course and the authors have paid particular attention to the presentation, clarity and arrangement of the material, making it ideally suited for independent study and classroom use. An important part of learning graph theory is problem solving; for this reason large numbers of examples, problems (with full solutions) and exercises (without solutions) are included.
Accompanying the book is a CD-ROM comprising a Graphs Database, containing all the simple unlabelled graphs with up to seven vertices, and a Graphs Editor that enables students to construct and manipulate graphs. Both the Database and Editor are simple to use and allow students to investigate graphs with ease. Computing Notes and suggested activities are provided.
... Read more

Book Description

Graph theory continues to be one of the fastest growing areas of modern mathematics because of its wide applicability in such diverse disciplines as computer science, engineering, chemistry, management science, social science, and resource planning. Graphs arise as mathematical models in these fields, and the theory of graphs provides a spectrum of methods of proof. This concisely written textbook is intended for an introductory course in graph theory for undergraduate mathematics majors or advanced undergraduate and graduate students from the many fields that benefit from graph-theoretic applications.

Customer Reviews (2)

There are much better Graph Theory Books
The errors in this text are unfortunate, and the presentation is not engaging. I did find that "A First look at Graph Theory" by Clark and Holton was useful and "Introduction to Graph Theory" by Chartrand and Zhang, was very readable.

Affordable but not accurate
It's nice to have an affordable math book, and this one does give a good introduction to graph theory.Unfortunately, there are also mistakes (some of which REALLY should have been caught in proofreading) which could confuse someone attempting to learn graph theory from this book.(These are both in the text and in the answers provided for the problems, such as giving the wrong number for the length of a path) ... Read more

Book Description

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.

Book Description
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 (1)

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

Book Description
The scope of graph theory is being increasingly felt because of its wide ranging applications in Computer Science, Computer Science, Communication Engineering and Management Science etc,. The last three decades have witnessed an upsurge of interest and activity in graph theory, particularly among applied mathematicians and engineers. Excellent textbooks and a good number of conference proceedings on graph theory are being published periodically all over the world. ... Read more

Book Description
This book is a concise, yet carefully written, introduction to modern graph theory, covering all its major recent developments. It can be used both as a reliable textbook for an introductory course and as a graduate text: on each topic it covers all the basic material in full detail, and adds one or two deeper results (again with detailed proofs) to illustrate the more advanced methods of that field.This second edition extends the first in two ways. It offers a thoroughly revised and updated chapter on graph minors, which now includes full new proofs of two of the central Robertson-Seymour theorems (as well as a detailed sketch of the entire proof of their celebrated Graph Minor Theorem). Second, there is now a section of hints for all the exercises, to enhance their value for both individual study and classroom use. ... Read more

Customer Reviews (4)

Dense reading
I have to read this book to prepare for a summer research program; however unfortunately for a high school student, this text is unreasonably concise with the proofs and makes for very tough independent study.

An exciting book.
Really, this book is very nice. It is simple to read (its language is quite easy) yet serious and precise. It covers many important aspects of the pure graph theory , leaving there applications and algorithms to an algorithmic graph theory book. So, to learn the core of the pure graph theory, this book is your choice, espesially if you are a computer science student (Because it dosen't deal deeply with tough mathematics).

Small yet comprehensive.
An excellent book. With minimum knowledge and an open mind, you can work rapidly throughout this book. I used it as a reference for some work I'm currently doing on the structure of extremal graphs and it came in very handy. To sum up, it's what you would normally expect from Springer's series on grad math texts.

Exellent Introduction
Almost no pre-requisites are needed for this book, (There is a shortsection which touches on Linear Alg, and another on very elementarytopology) and yet it will take you from the very basic notions, to researchlevel problems in this subject. It covers almost all the major notionsabout graphs, including coloring, matching, flows... Any reader is bound tofind the section on Ramsey theory especially interesting. However, infinitegraphs and Algebric graph theory are not covered.

There is a usefulcommentary on the references at the end of each chapter. ... Read more

Book Description

Book Description
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 in the field, can be used by mathematicians, computer scientists and electrical engineers, as well as people working in biomathematics. It is self contained, and with numerous exercises in each chapter, is ideal for advanced courses or self study. ... Read more

Customer Reviews (2)

Written by a Master in the Field
This is the second book by Dr. Bollobas that I have read, and it is clear, that Dr. Bollobas is a master in the field.
It is amazing, how few lines he needs to motivate the subject matter completely.
The gaps in the proofs were sometimes large for me, but then again, the audience he wishes to address are "research students and professional mathematicians", and I am only a hobby mathematician.

The only minus point are the large number of misprints: I counted over 130 of them, and this is not counting misprints like 'some' instead of 'same', etc. This is very annoying if one uses the book for self study.

(Unfortunaltely misprints seem Dr. Bollobas' problem: Also the other book I read: 'Modern Graph Theory' had more than its share)

For percolation thresholds?
The book can be of interest to those researchers studying such topics as percolation thresholds for conducting material distributed in a non-conducting matrix. The conducting material is assumed to be distributed in some random sense. And a general question might be what minimum average concentration will lead to a graph (or cluster) with a spatial extent comparable to the entire sample. The chapter on the diameter of graphs may lead to insight on this issue.

No doubt, readers might also imagine other applications for the book. It discusses "long paths" in a graph, and what type of distribution you might expect for these. Take some time in studying the chapters. ... Read more

Book Description
This book introduces graph theory, a subject with a wide range of applications in real-work situations. This book is designed to be easily accessible to the novice, assuming no more than a good grasp of algebra to understand and relate to the concepts presented. Using many examples, illustrations, and figures, it provides an excellent foundation for the basic knowledge of graphs and their applications.This book includes an introductory chapter that reviews the tools necessary to understand the concepts of graphs, and then goes on to cover such topics as trees and bipartite graphs, distance and connectivity, Eulerian and Hamiltonian graphs, graph coloring, matrices, algorithms, planar graphs, and digraphs and networks.Graph theory has a wide range of applications; this book is useful for those in the fields of anthropology, computer science, chemistry, environmental conservation, fluid dynamics, psychology, sociology, traffic management, telecommunications, and business managers and strategists. ... Read more

Customer Reviews (1)

It's a very good intro text.
Good choice of topics. Easy to read. The concepts are well motivated. The book is full of applications. An undergraduate will be able to follow the proofs. They are clear. I also liked the homework exercises. This is a student-friendly book, as the title suggests. ... Read more

Book Description
First published in 1976, this book has been widely acclaimed both for its significant contribution to the history of mathematics and for the way that it brings the subject alive. Building on a set of original writings from some of the founders of graph theory, the book traces the historical development of the subject through a linking commentary. The relevant underlying mathematics is also explained, providing an original introduction to the subject for students.From reviews: 'The book...serves as an excellent examplein fact, as a modelof a new approach to one aspect of mathematics, when mathematics is considered as a living, vital and developing tradition.' (Edward A. Maziark in Isis) 'Biggs, Lloyd and Wilson's unusual and remarkable book traces the evolution and development of graph theory...Conceived in a very original manner and obviously written with devotion and a very great amount of painstaking historical research, it contains an exceptionally fine collection of source material, and to a graph theorist it is a treasure chest of fascinating historical information and curiosities with rich food for thought.' (Gabriel Dirac in Centaurus) 'The lucidity, grace and wit of the writing makes this book a pleasure to read and re-read.' (S. H. Hollingdale in Bulletin of the Institute of Mathematics and its Applications) ... Read more

Customer Reviews (1)

Some interesting episodes from the history of graph theory
This book teaches basic graph theory through excerpts from original papers in English translation. In between, the authors discuss the history and the mathematical concepts at an elementary level, hoping that the book may serve as a first textbook of graph theory. I think it could serve this purpose very well. There is a lot of focus on the puzzle-style origins of graph theory, starting with marvelous 18th century classics of Euler and Vandermonde and then including many other charming little topics like for instance a very nice 1895 paper of Tarry on how to find your way out of a maze. There are also topics from other fields (e.g. chemistry), but here I think the background discussions are a bit weak. Something like half the book is centred around the four-colour problem, which is historically faithful and necessary, but it is obviously disturbing that the book ends long before this problem was solved. ... Read more

Book Description
An effort has been made to present the various topics in the theory of graphs in a logical order, to indicate the historical background, and to clarify the exposition by including figures to illustrate concepts and results. In addition, there are three appendices which provide diagrams of graphs, directed graphs, and trees. The emphasis throughout is on theorems rather than algorithms or applications, which however are occaisionally mentioned. ... Read more

Customer Reviews (4)

A class for theoretical math, but not applied math
I used this text in school, as a computer science student in a theoretical math class.

If you are looking for examples of computer algorithms, look elsewhere; the closest this will get you is to "existence proofs", which is showing that something (such as a hamiltonian cycle) exists in a graph that has thus-and-such number of points or edges, but not tell you which sequence of points/edges make up that something. (For example, a graph can be embedded in a plane unless there's a subgraph that looks like K(5) or K(3,3) inside it - this is in about chapter 5, and an important theorem. The text proves this, but doesn't tell you HOW to embed the graph in a plane.)

That said, this is an excellent book for theoretical mathematics. I understand that the first two chapters can be used as a high school math text, as an introduction to proofs, and agree that it would work well.

As a formal introduction to proving theorems, especially in a self-contained world (you don't need many prerequisites for this, like you do for a topology or analysis text), this is pretty swell.

So, to the person who said that he didn't like this because there weren't algorithms in the book: you can find those in the semiliterate computer science textbooks. (I would insist that the last four words of the previous sentence are redundant.)

Look here for mathematics.

missing solution
This book was not published in 1995, but in 1969.

i was looking for some algorithms that solve the classical problems like shortest path and they were not even mentioned

Clasical and Excellent
Good

The absolute classic!
This is the abslolute classic in the field and a great introduction to this fascinating area of the discrete mathematics. ... Read more

Book Description
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