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Spectral Graph Theory
Fan R. K. Chung, University of Pennsylvania, Philadelphia, PA
A co-publication of the AMS and CBMS.
cover
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CBMS Regional Conference Series in Mathematics
1997; 212 pp; softcover
Number: 92
Reprint/Revision History:
reprinted 1997 with corrections
ISBN-10: 0-8218-0315-8
ISBN-13: 978-0-8218-0315-8
List Price: US$32
Member Price: US$25.60
All Individuals: US$25.60
Order Code: CBMS/92
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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 well-written exposition can be likened to a conversation with a good teacher--one 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 graph--from Cheeger constants and diameters to more recent developments such as log-Sobolev constants and Harnack inequalities--are related to the spectrum.

"Even though the point of view of the book is quite geometric, the methods and exposition are purely graph-theoretic. 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 quasi-randomness
  • 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
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