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© 2012

Spectra of Graphs

Benefits

  • Provides an excellent introduction to advanced topics in graph spectral theory

  • Written by experts in this area

  • Includes tables, references, author and subject index

Textbook

Part of the Universitext book series (UTX)

Table of contents

  1. Front Matter
    Pages i-xiii
  2. Andries E. Brouwer, Willem H. Haemers
    Pages 1-20
  3. Andries E. Brouwer, Willem H. Haemers
    Pages 21-32
  4. Andries E. Brouwer, Willem H. Haemers
    Pages 33-66
  5. Andries E. Brouwer, Willem H. Haemers
    Pages 67-81
  6. Andries E. Brouwer, Willem H. Haemers
    Pages 83-91
  7. Andries E. Brouwer, Willem H. Haemers
    Pages 93-99
  8. Andries E. Brouwer, Willem H. Haemers
    Pages 101-104
  9. Andries E. Brouwer, Willem H. Haemers
    Pages 105-113
  10. Andries E. Brouwer, Willem H. Haemers
    Pages 115-149
  11. Andries E. Brouwer, Willem H. Haemers
    Pages 151-164
  12. Andries E. Brouwer, Willem H. Haemers
    Pages 165-175
  13. Andries E. Brouwer, Willem H. Haemers
    Pages 177-185
  14. Andries E. Brouwer, Willem H. Haemers
    Pages 187-197
  15. Andries E. Brouwer, Willem H. Haemers
    Pages 199-219
  16. Andries E. Brouwer, Willem H. Haemers
    Pages 221-227
  17. Back Matter
    Pages 229-250

About this book

Introduction

This book provides an elementary treatment of the basic material about graph spectra, both for ordinary, and Laplace and Seidel spectra. It covers standard topics such as bounds on the sizes of cliques and cocliques, chromatic number and Shannon capacity, the connection between randomness and the 'eigenvalue gap', and applications. It continues with a presentation of 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 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.

Keywords

Distance regular graph Graph spectrum Seidel spectra Strongly regular graph Trees

Authors and affiliations

  1. 1., Department of MathematicsEindhoven University of TechnologyEindhovenNetherlands
  2. 2., Department of Econometrics andTilburg UniversityTilburgNetherlands

Bibliographic information

Industry Sectors
Finance, Business & Banking

Reviews

From the reviews:

“Algebraic graph theory seeks logical relations between the graph structure and spectrum structure. Viewing graphs as matrices makes graph spectra a rich, nuanced branch of linear algebra, the central undergraduate subject. … the present volume offers the more thorough literature survey. Summing Up: Recommended. Upper-division undergraduates and above.” (D. V. Feldman, Choice, Vol. 49 (11), August, 2012)

“This book contains an extensive overview of current topics and recent developments in algebraic graph theory, and has a survey-like appearance. It is aimed primarily at researchers and graduate-level students, as it is based on lecture notes for the course that the authors gave at the Institute for Studies in Theoretical Physics and Mathematics in Tehran in 2006.” (Dragan Stevanović, Zentralblatt MATH, Vol. 1231, 2012)

“The theory of graph spectra has been getting increasing attention over the last several years. … This text … moves the study further along and provides an outstanding reference for graduate students and researchers interested in the many applications of these eigenvalues and their associated eigenvectors. … the authors are well-versed in the literature, providing 358 references and frequently noting where their definitions might differ slightly from those of some previous researchers. … the text serves more as a graduate-level monograph … .” (John T. Saccoman, The Mathematical Association of America, May, 2012)