Strongly Regular Graphs Derived from Combinatorial Designs

Publisher Summary This chapter explores strongly regular graphs derived from combinatorial designs. It presents graphs that are undirected, without loops, and without multiple edges. It discusses the use of adjacency matrices that have elements 0 on the diagonal, −1 or + 1 elsewhere accordingly as the corresponding vertices are adjacent or nonadjacent, respectively. The chapter presents a fiber-type construction method for graphs, which is applied to block designs with λ = 1 and yields strongly regular graphs. It also discusses block designs in which the number of points in the intersection of any pair of blocks attains only two values. The methods are applied to the construction of symmetric Hadamard matrices with constant diagonal. These matrices are related to special strong graphs. Symmetric Hadamard matrices with constant diagonal are involved in various current investigations.

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