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Spectra of Graphs

  • Andries E. Brouwer
  • Willem H. Haemers

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

  • Andries E. Brouwer
    • 1
  • Willem H. Haemers
    • 2
  1. 1., Department of MathematicsEindhoven University of TechnologyEindhovenNetherlands
  2. 2., Department of Econometrics andTilburg UniversityTilburgNetherlands

Bibliographic information

  • DOI https://doi.org/10.1007/978-1-4614-1939-6
  • Copyright Information Andries E. Brouwer and Willem H. Haemers 2012
  • Publisher Name Springer, New York, NY
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-1-4614-1938-9
  • Online ISBN 978-1-4614-1939-6
  • Series Print ISSN 0172-5939
  • Series Online ISSN 2191-6675
  • Buy this book on publisher's site