A Beginner’s Guide to Graph Theory

  • W. D. Wallis

Table of contents

  1. Front Matter
    Pages i-xix
  2. W. D. Wallis
    Pages 1-18
  3. W. D. Wallis
    Pages 19-42
  4. W. D. Wallis
    Pages 43-51
  5. W. D. Wallis
    Pages 53-64
  6. W. D. Wallis
    Pages 65-76
  7. W. D. Wallis
    Pages 77-91
  8. W. D. Wallis
    Pages 93-111
  9. W. D. Wallis
    Pages 113-122
  10. W. D. Wallis
    Pages 123-138
  11. W. D. Wallis
    Pages 139-153
  12. W. D. Wallis
    Pages 155-165
  13. W. D. Wallis
    Pages 167-179
  14. W. D. Wallis
    Pages 181-204
  15. W. D. Wallis
    Pages 205-215
  16. W. D. Wallis
    Pages 217-224
  17. Back Matter
    Pages 225-260

About this book

Introduction

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.

Key features:

* Introductory chapters present the main ideas and topics in graph theory—walks, paths and cycles, radius, diameter, eccentricity, cuts and connectivity, trees

* Subsequent chapters examine specialized topics and applications

* Numerous examples and illustrations

* Comprehensive index and bibliography, with suggested literature for more advanced material

New to the second edition:

* New chapters on labeling and on communications networks and small-worlds

* Expanded beginner’s material in the early chapters, including more examples, exercises, hints and solutions to key problems

* Many additional changes, improvements, and corrections throughout resulting from classroom use and feedback

Striking a balance between a theoretical and practical approach with a distinctly applied flavor, this gentle introduction to graph theory consists of carefully chosen topics to develop graph-theoretic reasoning for a mixed audience. Familiarity with the basic concepts of set theory, along with some background in matrices and algebra, and a little mathematical maturity are the only prerequisites.

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From a review of the first edition:

"Altogether the book gives a comprehensive introduction to graphs, their theory and their application…The use of the text is optimized when the exercises are solved. The obtained skills improve understanding of graph theory as well… It is very useful that the solutions of these exercises are collected in an appendix."

—Simulation News Europe

Keywords

Addition Graph Sim combinatorics graph theory management science network engineering set theory

Authors and affiliations

  • W. D. Wallis
    • 1
  1. 1.Department of MathematicsSouthern Illinois UniversityCarbondaleUSA

Bibliographic information

  • DOI https://doi.org/10.1007/978-0-8176-4580-9
  • Copyright Information Birkhäuser Boston 2007
  • Publisher Name Birkhäuser Boston
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-0-8176-4484-0
  • Online ISBN 978-0-8176-4580-9
  • About this book