New directed strongly regular graphs on 60 vertices

TL;DR

This paper proves the existence of several new directed strongly regular graphs with specific parameters on 60 vertices, utilizing group actions for their construction.

Contribution

It introduces new directed strongly regular graphs with particular parameters, constructed via the action of the group S_5 × 2.

Findings

Existence of directed strongly regular graphs with parameters (60,21,11,6,8), (60,22,12,8,8), (60,24,10,9,10), (60,25,17,8,12), (60,27,21,12,12), (60,28,20,14,12)

Group S_5 × 2 acts transitively on these graphs

Provides explicit constructions for these graphs

Abstract

We prove the existence of directed strongly regular graphs with parameters (60,21,11,6,8), (60,22,12,8,8), (60,24,10,9,10), (60,25,17,8,12), (60,27,21,12,12) and (60,28,20,14,12). The group $S_5 \times 2$ acts transitively on the constructed graphs.