Strongly Regular Graphs Derived from Combinatorial Designs

Several concepts in discrete mathematics such as block designs, Latin squares, Hadamard matrices, tactical configurations, errorcorrecting codes, geometric configurations, finite groups, and graphs are by no means independent. Combinations of these notions may serve the development of any one of them, and sometimes reveal hidden interrelations. In the present paper a central role in this respect is played by the notion of strongly regular graph, the definition of which is recalled below. In § 2, a fibre-type construction for graphs is given which, applied to block designs with λ = 1 and Hadamard matrices, yields strongly regular graphs. The method, although still limited in its applications, may serve further developments. In § 3 we deal with block designs, first considered by Shrikhande [22], in which the number of points in the intersection of any pair of blocks attains only two values.