Distance-Regular Graphs

1. Front Matter

   Pages i-xvii

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2. Special Regular Graphs

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

   Pages 1-42

3. Association Schemes

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

   Pages 43-78

4. Representation Theory

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

   Pages 79-125

5. Theory of Distance-Regular Graphs

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

   Pages 126-166

6. Parameter Restrictions for Distance-Regular Graphs

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

   Pages 167-192

7. Classification of the Known Distance-Regular Graphs

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

   Pages 193-213

8. Distance-Transitive Graphs

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

   Pages 214-234

9. Q-polynomial Distance-Regular Graphs

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

   Pages 235-254

10. The Families of Graphs with Classical Parameters

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

    Pages 255-293

11. Graphs of Coxeter and Lie Type

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

    Pages 294-344

12. Graphs Related to Codes

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

    Pages 345-373

13. Graphs Related to Classical Geometries

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

    Pages 374-390

14. Sporadic Graphs

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

    Pages 391-412

15. Tables of Parameters for Distance Regular Graphs

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

    Pages 413-432

16. Back Matter

    Pages 433-495

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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.

• Arithmetic
• Lie
• geometry
• mathematics
• proof
• symmetric relation
• combinatorics

• Centrum voor Wiskunde en Informatica, Stichting Mathematisch Centrum, Amsterdam, The Netherlands

  Andries E. Brouwer, Arjeh M. Cohen

• Institut für Angewandte Mathematik, Universität Freiburg, Freiburg im Breisgau, Germany

  Arnold Neumaier

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