The rapidly expanding area of algebraic graph theory uses two different branches of algebra to explore various aspects of graph theory: linear algebra (for spectral theory) and group theory (for studying graph symmetry). These areas have links with other areas of mathematics, such as logic and harmonic analysis, and are increasingly being used in such areas as computer networks where symmetry is an important feature. Other books cover portions of this material, but this book is unusual in covering both of these aspects and there are no other books with such a wide scope. Peter J. Cameron, internationally recognized for his substantial contributions to the area, served as academic consultant for this volume, and the result is ten expository chapters written by acknowledged international experts in the field. Their well-written contributions have been carefully edited to enhance readability and to standardize the chapter structure, terminology and notation throughout the book. To help the reader, there is an extensive introductory chapter that covers the basic background material in graph theory, linear algebra and group theory. Each chapter concludes with an extensive list of references.

Foreword Peter J. Cameron; Introduction; 1. Eigenvalues of graphs Michael Doob; 2. Graphs and matrices Richard A. Brualdi and Bryan L. Shader; 3. Spectral graph theory Dragos Cvetkovic and Peter Rowlinson; 4. Graph Laplacians Bojan Mohar; 5. Automorphism groups Peter J. Cameron; 6. Cayley graphs Brian Alspach; 7. Finite symmetric graphs Cheryle E. Praeger; 8. Strongly regular graphs Peter J. Cameron; 9. Distance-transitive graphs Arjeh M. Cohen; 10. Computing with graphs and groups Leonard H. Soicher.