Strongly Regular Graphs

This monograph on strongly regular graphs is an invaluable reference for anybody working in algebraic combinatorics.

Andries E. Brouwer (Author), H. Van Maldeghem (Author)

9781316512036, Cambridge University Press

Hardback, published 13 January 2022

425 pages
24.1 x 16.1 x 3.5 cm, 0.91 kg

'This is a book the mathematics world has long been waiting for … [The book] is by two of the leading researchers in the field. An interested reader will find almost everything on strongly regular graphs.' Ulrich Tamm, MathSciNet

Strongly regular graphs lie at the intersection of statistical design, group theory, finite geometry, information and coding theory, and extremal combinatorics. This monograph collects all the major known results together for the first time in book form, creating an invaluable text that researchers in algebraic combinatorics and related areas will refer to for years to come. The book covers the theory of strongly regular graphs, polar graphs, rank 3 graphs associated to buildings and Fischer groups, cyclotomic graphs, two-weight codes and graphs related to combinatorial configurations such as Latin squares, quasi-symmetric designs and spherical designs. It gives the complete classification of rank 3 graphs, including some new constructions. More than 100 graphs are treated individually. Some unified and streamlined proofs are featured, along with original material including a new approach to the (affine) half spin graphs of rank 5 hyperbolic polar spaces.

1. Graphs
2. Polar spaces
3. Graphs related to polar spaces
4. Buildings
5. Fischer spaces
6. Golay codes, Witt designs, and Leech lattice
7. Cyclotomic constructions
8. Combinatorial constructions
9. p-Ranks
10. Individual graph descriptions
11. Classification of rank 3 graphs
12. Parameter table
References
Parameter Index
Author Index
Subject Index.

Subject Areas: Combinatorics & graph theory [PBV], Geometry [PBM], Discrete mathematics [PBD], Coding theory & cryptology [GPJ], Information theory [GPF]