New versions of the Wallis-Fon-Der-Flaass construction to create divisible design graphs

Abstract

A k-regular graph on v vertices is a divisible design graph with parameters (v, k, lambda_1 ,lambda_2, m, n) if its vertex set can be partitioned into m classes of size n, such that any two different vertices from the same class have lambda_1 common neighbours, and any two vertices from different classes have lambda_2 common neighbours whenever it is not complete or edgeless. If m=1, then a divisible design graph is strongly regular with parameters (v, k, lambda_1, lambda_1). In this paper the Wallis-Fon-Der-Flaass construction of strongly regular graphs is modified to create new constructions of divisible design graphs. In some cases, these constructions lead to strongly regular graphs.