1 - Graphs

Summary

The first chapter contains the basics of the theory of strongly regular graphs. In particular all basic notions such as parameters and spectrum are rigorously defined. The standard example such as Johnson graphs, Hamming graphs, Paley graphs are introduced. We treat Seidel switching and regular two-graphs, (induced) subgraphs, strongly regular graphs with smallest eigenvalue —2, regular partitions and regular (intriguing) sets. We enumerate the small examples and discuss prolific constructions. This chapter also contains an introduction to two slightly more general objects needed in the book: distance regular graphs (including the main examples, and a discussion on imprimitivity), and association schemes and coherent configurations (including a brief discussion of the Bose-Mesner algebra, linear programming bound, code-clique theorem, Krein parameters, Euclidean representation, subschemas, the absolute bound and the mu-bound).