Construction of directed strongly regular graphs with nontrivial automorphisms

TL;DR

This paper introduces a new method for constructing directed strongly regular graphs with specific parameters, resulting in the first known examples and a classification of automorphisms of prime order.

Contribution

It presents a novel construction technique for directed strongly regular graphs and provides the first examples with parameters (22,9,6,3,4), including classification of automorphisms.

Findings

First examples of directed strongly regular graphs with parameters (22,9,6,3,4)

Automorphisms of prime order are limited to order two or three

Constructed and classified 472 such graphs with automorphism of order three

Abstract

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.