A Beginner's Guide to Graph Theory

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

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