Once considered an “unimportant” branch of topology, graph theory has come into its own through many important contributions to a wide range of fields – and is now one of the fastest-growing areas in discrete mathematics and computer science. This practical, intuitive book introduces basic concepts, definitions, theorems, and examples from graph theory. Presents a collection of interesting results from mathematics that involve key concepts and proof techniques. Covers design and analysis of computer algorithms for solving problems in graph theory. Discusses applications of graph theory to the sciences. Includes a collection of graph algorithms, written in Java, that are ready for compiling and running. For anyone interested in learning graph theory, discrete structures, or algorithmic design for graph problems.

Preface                                                                                                     

1     Introduction to Graph Theory                                               

2     Basic Concepts in Graph Theory                                      

3     TreesandForests

4     Spanning Trees

5     Fundamental Properties of Graphs and Digraphs

6     Connectivity and Flow

7     Planar Graphs

8     Graph Coloring

9     Coloring Enumerations and Chordal Graphs

10    Independence,Dominance, and Matchings  

11    Cover Parameters and MatchingPolynomials

12    GraphCounting

13    Graph Algorithms

APPENDICES

A Greek Alphabet

B Notation

C Top Ten Online References

Index ix