Strongly Regular Graphs (Encyclopedia of Mathematics and its Applications, Series Number 182)

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. Strongly regular graphs are found in statistical design, finite group theory, coding theory and quantum information theory. This detailed survey of the theory and examples gathers the major results for the first time. It is an invaluable reference for researchers in graph theory, algebraic combinatorics, information theory and group theory.