- Membership
- Publications
- Meetings
- Competitions
- Community
- Programs
- Students
- High School Teachers
- Faculty and Departments
- Underrepresented Groups
- MAA Awards
- MAA Grants

- News
- About MAA

Publisher:

Chapman & Hall/CRC

Publication Date:

2011

Number of Pages:

586

Format:

Hardcover

Edition:

5

Price:

89.95

ISBN:

9781439826270

Category:

Textbook

The Basic Library List Committee considers this book essential for undergraduate mathematics libraries.

[Reviewed by , on ]

John T. Saccoman

06/11/2012

Gary Chartrand has influenced the world of Graph Theory for almost half a century. He has supervised more than a score of Ph.D. dissertations and written several books on the subject. The most widely-known of these texts, *Graphs and Digraphs*, was coauthored in earlier editions with former student Linda Lesniak, and they have added their frequent collaborator Ping Zhang as a coauthor in the most recent edition. The text has much to recommend it, with a clear exposition, and numerous challenging examples make it an ideal textbook for the advanced undergraduate or beginning graduate course.

The authors have updated their notation to reflect the current practice in this still-growing area of study. By the authors’ estimation, the 5^{th} edition is approximately 50% longer than the 4^{th} edition.

Among the changes in the 5^{th} edition are three separate chapters for vertex, map and edge colorings, expanded coverage of domination, matchings and extremal graph theory. In addition, the new version contains sections on perfect graphs, cages and historical figures of graph theory.

In the section on historical figures of graph theory, the legendary Frank Harary, author of the second graph theory text ever produced, is one of the figures profiled. His book was the standard in the discipline for several decades. Chartrand, Lesniak and Zhang have produced a worthy successor.

John T. Saccoman is Professor of Mathematics at Seton Hall University in South Orange, NJ

**Introduction to Graphs**Graphs and Subgraphs

Degree Sequences

Connected Graphs and Distance

Multigraphs and Digraphs

**Trees and Connectivity**Nonseparable Graphs

Trees

Spanning Trees

Connectivity and Edge-Connectivity

Menger’s Theorem

**Eulerian and Hamiltonian Graphs**Eulerian Graphs

Hamiltonian Graphs

Powers of Graphs and Line Graphs

**Digraphs**Strong Digraphs

Tournaments

Flows in Networks

**Graphs: History and Symmetry **Some Historical Figures of Graph Theory

The Automorphism Group of a Graph

Cayley Color Graphs

The Reconstruction Problem

**Planar Graphs**The Euler Identity

Planarity versus Nonplanarity

The Crossing Number of a Graph

Hamiltonian Planar Graphs

**Graph Embeddings**The Genus of a Graph

2-Cell Embeddings of Graphs

The Maximum Genus of a Graph

The Graph Minor Theorem

**Vertex Colorings**The Chromatic Number of a Graph

Color-Critical Graphs

Bounds for the Chromatic Number

Perfect Graphs

List Colorings

**Map Colorings**The Four Color Problem

Colorings of Planar Graphs

The Conjectures of Hajós and Hadwiger

Chromatic Polynomials

The Heawood Map-Coloring Problem

**Matchings, Factorization, and Domination **Matchings and Independence in Graphs

Factorization

Decomposition and Graceful Graphs

Domination

**Edge Colorings**Chromatic Index and Vizing’s Theorem

Class One and Class Two Graphs

Tait Colorings

Nowhere-Zero Flows

List Edge Colorings and Total Colorings

**Extremal Graph Theory**Turán’s Theorem

Cages

Ramsey Theory

**Hints and Solutions to Odd-Numbered ExercisesBibliography Index of Names Index of Mathematical Terms List of Symbols**

- Log in to post comments