Sporadic Examples of Directed Strongly Regular Graphs Obtained by Computer Algebra Experimentation (Extended version)

TL;DR

This paper uses computer algebra tools to construct new directed strongly regular graphs by exploring non-commutative association schemes and Cayley graphs over non-Abelian groups, discovering examples for previously unknown parameter sets.

Contribution

It introduces novel computational techniques for constructing directed strongly regular graphs using non-commutative algebraic structures, expanding known existence results.

Findings

28 new directed strongly regular graphs identified

Examples for previously unknown parameter sets provided

Demonstrates effectiveness of computer algebra in graph construction

Abstract

We report about the results of the application of modern computer algebra tools for construction of directed strongly regular graphs. The suggested techniques are based on the investigation of non-commutative association schemes and Cayley graphs over non-Abelian groups. We demonstrate examples of directed strongly regular graphs for 28 different parameter sets, for which the existence of a corresponding digraph has not been known before.