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 first examples 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.