New infinite families of directed strongly regular graphs via equitable partitions

TL;DR

This paper presents a method to generate infinite families of directed strongly regular graphs using equitable partitions, confirming the existence of many previously unknown graphs with specific parameters.

Contribution

It introduces a novel construction technique for DSRGs based on equitable partitions, expanding the known catalog of such graphs.

Findings

Constructed dozens of infinite DSRG families

Confirmed existence of DSRGs for 30 previously open parameter sets

Validated the method for graphs up to order 110

Abstract

In this paper we introduce a construction of directed strongly regular graphs from smaller ones using equitable partitions. Each equitable partition of a single DSRG satisfying several conditions leads to an infinite family of directed strongly regular graphs. We construct in this way dozens of infinite families. For order at most 110, we confirm the existence of DSRGs for 30 previously open parameter sets.