Construction of directed strongly regular graphs with nontrivial automorphisms

In this paper we present a method for constructing directed strongly regular graphs with assumed action of an automorphism group. The application of this method leads to the construction of directed strongly regular graphs with parameters (22, 9, 6, 3, 4). We have shown that an automorphism of prime order acting on such a graph can only be of order two or three. Furthermore, we have constructed 472 directed strongly regular graphs with parameters (22, 9, 6, 3, 4) and classified all these graphs with an automorphism of order three.