Construction of strongly regular graphs using affine designs

Abstract

Suppose there exist a balanced incomplete block design with λ = 1 and an affine resolvable balanced incomplete block design, the two designs having the same replication number. Combining these designs we construct two strongly regular graphs. This is applied to give a new family of design graphs ((v, k, λ)-graphs). Finally, we show that for any prime power n there are two non-isomorphic design graphs with v = n2(n+2), k = n(n+1) and λ = n.