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.
This book gives an elementary treatment of the basic material about graph spectra, both for ordinary, and Laplace and Seidel spectra. The text progresses systematically, by covering standard topics be
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 re
