• Graph theory continues to be one of the fastest growing areas of modern mathematics
• Second edition includes new chapters, more examples, exercises, hints and solutions to key problems
• Strikes a balance between a theoretical and practical approach

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.

Written for: Undergraduate mathematics majors, as well as advanced undergraduates and graduate students in computer science, engineering, chemistry, management science, social science, and resource planning

• List of Figures
• 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
• Communication Networks and Small Worlds
• References
• Hints
• Answers and Solutions