Divisible design digraphs

Abstract

Divisible design graphs (DDGs) have been recently defined by Haemers, Kharaghani, and Meulenberg as a generalization of (υ, κ, λ)-graphs. In this paper we define and study divisible design digraphs (DDDs), a directed graph version of DDGs. On the other hand, DDDs are also natural generalization of doubly regular asymmetric digraphs. We obtain necessary conditions for the existence of a DDD with given parameters and give some constructions.