# A Beginner's Guide to Graph Theory

Springer Science & Business Media, May 5, 2010 - Mathematics - 260 pages

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 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

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### Contents

 1 Graphs 1 2 Walks Paths and Cycles 19 3 Connectivity 43 4 Trees 53 5 Linear Spaces Associated with Graphs 65 6 Factorizations 77 7 Graph Colorings 92 8 Planarity 113
 11 Digraphs 154 12 Critical Paths 167 13 Flows in Networks 180 14 Computational Considerations 205 15 Communications Networks and SmallWorlds 217 References 225 Hints 230 Answers and Solutions 235

 9 Labeling 123 10 Ramsey Theory 139