Distance-Regular Graphs

  • Andries E. Brouwer
  • Arjeh M. Cohen
  • Arnold Neumaier

Part of the Ergebnisse der Mathematik und ihrer Grenzgebiete book series (MATHE3, volume 18)

Table of contents

  1. Front Matter
    Pages i-xvii
  2. Andries E. Brouwer, Arjeh M. Cohen, Arnold Neumaier
    Pages 1-42
  3. Andries E. Brouwer, Arjeh M. Cohen, Arnold Neumaier
    Pages 43-78
  4. Andries E. Brouwer, Arjeh M. Cohen, Arnold Neumaier
    Pages 79-125
  5. Andries E. Brouwer, Arjeh M. Cohen, Arnold Neumaier
    Pages 126-166
  6. Andries E. Brouwer, Arjeh M. Cohen, Arnold Neumaier
    Pages 167-192
  7. Andries E. Brouwer, Arjeh M. Cohen, Arnold Neumaier
    Pages 193-213
  8. Andries E. Brouwer, Arjeh M. Cohen, Arnold Neumaier
    Pages 214-234
  9. Andries E. Brouwer, Arjeh M. Cohen, Arnold Neumaier
    Pages 235-254
  10. Andries E. Brouwer, Arjeh M. Cohen, Arnold Neumaier
    Pages 255-293
  11. Andries E. Brouwer, Arjeh M. Cohen, Arnold Neumaier
    Pages 294-344
  12. Andries E. Brouwer, Arjeh M. Cohen, Arnold Neumaier
    Pages 345-373
  13. Andries E. Brouwer, Arjeh M. Cohen, Arnold Neumaier
    Pages 374-390
  14. Andries E. Brouwer, Arjeh M. Cohen, Arnold Neumaier
    Pages 391-412
  15. Andries E. Brouwer, Arjeh M. Cohen, Arnold Neumaier
    Pages 413-432
  16. Back Matter
    Pages 433-495

About this book

Introduction

Ever since the discovery of the five platonic solids in ancient times, the study of symmetry and regularity has been one of the most fascinating aspects of mathematics. Quite often the arithmetical regularity properties of an object imply its uniqueness and the existence of many symmetries. This interplay between regularity and symmetry properties of graphs is the theme of this book. Starting from very elementary regularity properties, the concept of a distance-regular graph arises naturally as a common setting for regular graphs which are extremal in one sense or another. Several other important regular combinatorial structures are then shown to be equivalent to special families of distance-regular graphs. Other subjects of more general interest, such as regularity and extremal properties in graphs, association schemes, representations of graphs in euclidean space, groups and geometries of Lie type, groups acting on graphs, and codes are covered independently. Many new results and proofs and more than 750 references increase the encyclopaedic value of this book.

Keywords

Arithmetic Lie geometry mathematics proof symmetric relation

Authors and affiliations

  • Andries E. Brouwer
    • 1
  • Arjeh M. Cohen
    • 1
  • Arnold Neumaier
    • 2
  1. 1.Centrum voor Wiskunde en InformaticaStichting Mathematisch CentrumAmsterdamThe Netherlands
  2. 2.Institut für Angewandte MathematikUniversität FreiburgFreiburg im BreisgauGermany

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-642-74341-2
  • Copyright Information Springer-Verlag Berlin Heidelberg 1989
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Springer Book Archive
  • Print ISBN 978-3-642-74343-6
  • Online ISBN 978-3-642-74341-2
  • Series Print ISSN 0071-1136
  • About this book