Spectra of Graphs

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Springer Science & Business Media, Dec 17, 2011 - Mathematics - 250 pages
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This book gives an elementary treatment of the basic material about graph spectra, both for ordinary, and Laplace and Seidel spectra. The text progresses systematically, by covering standard topics before presenting some new material on trees, strongly regular graphs, two-graphs, association schemes, p-ranks of configurations and similar topics. Exercises at the end of each chapter provide practice and vary from easy yet interesting applications of the treated theory, to little excursions into related topics. Tables, references at the end of the book, an author and subject index enrich the text.

Spectra of Graphs is written for researchers, teachers and graduate students interested in graph spectra. The reader is assumed to be familiar with basic linear algebra and eigenvalues, although some more advanced topics in linear algebra, like the Perron-Frobenius theorem and eigenvalue interlacing are included.

 

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Contents

Chapter 1 Graph Spectrum
1
Chapter 2 Linear Algebra
21
Chapter 3 Eigenvalues and Eigenvectors of Graphs
33
Chapter 4 The SecondLargest Eigenvalue
67
Chapter 5 Trees
83
Chapter 6 Groups and Graphs
93
Chapter 7 Topology
101
Chapter 8 Euclidean Representations
105
Chapter 11 Association Schemes
165
Chapter 12 DistanceRegular Graphs
177
Chapter 13 pranks
187
Chapter 14 Spectral Characterizations
199
Chapter 15 Graphs with Few Eigenvalues
221
References
229
Author Index
243
Subject Index
247

Chapter 9 Strongly Regular Graphs
115
Chapter 10 Regular Twographs
151

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