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.

This second edition includes new chapters on labeling and communications networks and small-worlds, as well as expanded beginner's material in the early chapters, including more examples, exercises, hints and solutions to key problems. Many additional changes, improvements, and corrections resulting from classroom use and feedback have been added throughout.

Graphs.- Walks, Paths and Cycles.- Connectivity.- Trees.- Linear Spaces Associated with Graphs.- Factorizations.- Graph Colorings.- Planarity.- Labeling.- Ramsey Theory.- Digraphs.- Critical Paths.- Flows in Networks.- Computational Considerations.- Communications Networks and Small-Worlds.