CBMS Regional Conference Series in Mathematics 1997; 212 pp; softcover Number: 92 Reprint/Revision History: reprinted 1997 with corrections ISBN10: 0821803158 ISBN13: 9780821803158 List Price: US$32 Member Price: US$25.60 All Individuals: US$25.60 Order Code: CBMS/92
 Beautifully written and elegantly presented, this book is based on 10 lectures given at the CBMS workshop on spectral graph theory in June 1994 at Fresno State University. Chung's wellwritten exposition can be likened to a conversation with a good teacherone who not only gives you the facts, but tells you what is really going on, why it is worth doing, and how it is related to familiar ideas in other areas. The monograph is accessible to the nonexpert who is interested in reading about this evolving area of mathematics. Readership Graduate students and research mathematicians interested in graph theory and its relations to combinatorics, geometry, communication theory, computer science, algebra, and other areas of pure and applied mathematics. Reviews "The book presents a very complete picture of how various properties of a graphfrom Cheeger constants and diameters to more recent developments such as logSobolev constants and Harnack inequalitiesare related to the spectrum. "Even though the point of view of the book is quite geometric, the methods and exposition are purely graphtheoretic. As a result, the book is quite accessible to a reader who does not have any background in geometry. "As the author writes, `the underlying mathematics of spectral graph theory through all its connections to the pure and applied, the continuous and discrete, can be viewed as a single unified subject.' "Anyone who finds this sentence appealing is encouraged to give this book a try. He or she will not be disappointed."  Mathematical Reviews "Incorporates a great deal of recent work, much of it due to the author herself ... clear, without being pedantic, and challenging, without being obscure."  Bulletin of the London Mathematical Society Table of Contents  Eigenvalues and the Laplacian of a graph
 Isoperimetric problems
 Diameters and eigenvalues
 Paths, flows, and routing
 Eigenvalues and quasirandomness
 Expanders and explicit constructions
 Eigenvalues of symmetrical graphs
 Eigenvalues of subgraphs with boundary conditions
 Harnack inequalities
 Heat kernels
 Sobolev inequalities
 Advanced techniques for random walks on graphs
 Bibliography
 Index
