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Last Edited
13 Sep 2009


Aaron D. Gross
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Graph Theory

Textbooks and Resources

The website is sponsored by the mathematical textbooks of Professor Jonathan Gross of Columbia University. It provides comprehensive graph theory resources maintained by Daniel Sanders.

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Bled'11 - 7th Slovenian International Conference on Graph Theory

19-25 June 2011
Bled, Slovenia


11 November 2007

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For Use With This New Text:

Combinatorial Methods Toolkit



Combinatorial Methods with Computer Applications

List Price: $99.95
Cat. #: C7435
ISBN: 9781584887430
ISBN 10: 1584887435
Publication Date: 11/8/2007
Number of Pages: 664
Availability: Not Yet Published


  • Provides a thorough, up-to-date treatment of combinatorics that covers topics such as asymptotics, graphs, and evaluating sums
  • Presents the computer algorithms in easy-to-read pseudo-code
  • Foreshadows difficult topics early in the book to prepare students for more in-depth discussions later on
  • Incorporates definitions, theorems, proofs, examples, and nearly 300 illustrations as pedagogical elements of the exposition
  • Includes numerous problems, along with many solutions and hints, that range from the reinforcement of basic skills to creative problem solving
  • Offers a companion website that contains extensive graph theory informational resources as well as a computational engine to help with calculations for some of the exercises

    Combinatorial Methods with Computer Applications provides in-depth coverage of recurrences, generating functions, partitions, and permutations, along with some of the most interesting graph and network topics, design constructions, and finite geometries. Requiring only a foundation in discrete mathematics, it can serve as the textbook in a combinatorial methods course or in a combined graph theory and combinatorics course.

    After an introduction to combinatorics, the book explores six systematic approaches within a comprehensive framework: sequences, solving recurrences, evaluating summation expressions, binomial coefficients, partitions and permutations, and integer methods. The author then focuses on graph theory, covering topics such as trees, isomorphism, automorphism, planarity, coloring, and network flows. The final chapters discuss automorphism groups in algebraic counting methods and describe combinatorial designs, including Latin squares, block designs, projective planes, and affine planes. In addition, the appendix supplies background material on relations, functions, algebraic systems, finite fields, and vector spaces.

    Paving the way for students to understand and perform combinatorial calculations, this accessible text presents the discrete methods necessary for applications to algorithmic analysis, performance evaluation, and statistics as well as for the solution of combinatorial problems in engineering and the social sciences.

  • New
    22 September 2005

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    Graph Theory and Its Applications --  2nd Edition

    ISBN: 158488505X
    Pub Date:
    Number of Pages: 800
    List Price: $84.95


    • Offers a comprehensive but accessible, applications-driven treatment of graph theory suitable for a variety of graduate and advanced undergraduate courses
    • Provides better coverage of algorithms and algebraic and topological graph theory than any other text
    • Supplies hundreds of drawings that promote spatial intuition
    • Incorporates several levels of carefully designed exercises that promote students' retention and develop and sharpen their problem-solving skills
    Already an international bestseller, with the release of this greatly enhanced second edition, Graph Theory and Its Applications is now an even better choice as a textbook for a variety of courses -- a textbook that will continue to serve your students as a reference for years to come.

    The superior explanations, broad coverage, and abundance of illustrations and exercises that positioned this as the premier graph theory text remain, but are now augmented by a broad range of improvements. Nearly 200 pages have been added for this edition, including nine new sections and hundreds of new exercises, mostly non-routine.

    What else is new?
    • New chapters on measurement and analytic graph theory
    • Supplementary exercises in each chapter - ideal for reinforcing, reviewing, and testing.
    • Solutions and hints, often illustrated with figures, to selected exercises - nearly 50 pages worth
    • Reorganization and extensive revisions in more than half of the existing chapters for smoother flow of the exposition
    • Foreshadowing - the first three chapters now preview a number of concepts, mostly via the exercises, to pique the interest of reader
    Gross and Yellen take a comprehensive approach to graph theory that integrates careful exposition of classical developments with emerging methods, models, and practical needs. Their 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.


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    Table of Contents
    New! (July 2004)


    Handbook of Graph Theory

    Jonathan L Gross
    Columbia University, New York, New York, USA

    Jay Yellen
    Rollins College, Winter Park, Florida, USA

    Series: Discrete Mathematics and Its Applications Volume: 25

    Cat. #: 8522
    Number of Pages: 1192
    ISBN: 1584880902
    List Price: $119.95
    Publication Date: 12/29/2003


    • Provides a unified, up-to-date resource on graph theory
    • Explores the algorithmic and optimization approaches of graph theory as well as "pure" graph theory
    • Unifies the diversity of graph theory terminology and notation
    • Bridges theory and practice with many easy-to-read algorithms

    Includes a glossary in each chapter-more than 1000 entries in total

    The Handbook of Graph Theory is the most comprehensive single-source guide to graph theory ever published. Best-selling authors Jonathan Gross and Jay Yellen assembled an outstanding team of experts to contribute overviews of more than 50 of the most significant topics in graph theory-including those related to algorithmic and optimization approaches as well as "pure" graph theory. They then carefully edited the compilation to produce a unified, authoritative work ideal for ready reference.

    Designed and edited with non-experts in mind, the Handbook of Graph Theory makes information easy to find and easy to understand. The treatment of each topic includes lists of essential definitions and facts accompanied by examples, tables, remarks, and in some areas, conjectures and open problems. Each section contains a glossary of terms relevant to that topic and an extensive bibliography of references that collectively form an extensive guide to the primary research literature.

    " excellent vehicle for either a class text or a self-study reference. The writing is clear... highly recommended text on graph theory that is most suitable for an advanced undergraduate in either engineering or computer science."

    -Journal of Mathematical Psychology



    topological graph theory

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    Topological Graph Theory

    JUNE 2001

    From Book News, Inc.
    This is a reprint of a work published in 1987, by John Wiley & Sons, with a brief new preface by the two authors and a new supplementary bibliography aimed at helping readers track recent trends in the field. Still solid after more than a decade, the book introduces the foundations and basic issues of topological graph theory, emphasizing graph embedding, but also covering the connections between topological graph theory and other areas of mathematics. Intended for first-year graduate students, students with a background in undergraduate discrete mathematics, and mathematicians, statisticians, and computer scientists needing a reference.Book News, Inc., Portland, OR

    The publisher, John Wiley & Sons
    This definitive treatment written by well-known experts emphasizes graph imbedding while providing thorough coverage of the connections between topological graph theory and other areas of mathematics: spaces, finite groups, combinatorial algorithms, graphical enumeration, and block design. Almost every result of studies in this field is covered, including most proofs and methods. Its numerous examples and clear presentation simplify conceptually difficult material, making the text accessible to... read more --This text refers to an out of print or unavailable edition of this title.

    Book Description
    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 theorema proof that revolutionized the field of graph theoryand examine the genus of a group, including imbeddings of Cayley graphs. 1987 edition. Many figures.



    We are pleased to announce a collaboration with Daniel Sanders, who will now maintain the Graph Theory Resources section of this site.  His previous graph theory page was noted as the AEI December, 1997, Mathematics of Computing Cool Site

    --Jonathan Gross and Jay Yellen

    January 2002
    #1 bestseller in graph theory on Barnes & Noble's website for all or part of every month since April 2001, among 411 titles listed.  

    Graph Theory and Its Applications is ranked #1 by in sales for graph theory titles.  Barnes & Noble's website offers the title for $74.95.  Please visit our ORDER page.


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