Construction of infinite families of vertex-transitive directed strongly regular graphs

Abstract

We introduce an innite family of permutation groups, which are the complete automor-phism groups of two dierent families of directed strongly regular graphs. For both families,there is a cyclic subgroup of the permutation group which acts semiregularly on the set of vertices of the directed graph and has two orbits. One of the two series gives an innite number ofdirected strongly regular graphs admitting a cyclic semiregular automorphism group with anstructure and an automorphism group for which only three sporadic examples were previouslyknown.