Some families of directed strongly regular graphs obtained from certain finite incidence structures

TL;DR

This paper presents new infinite families of directed strongly regular graphs constructed from specific antiflag collections of tactical configurations, expanding the known classes of such graphs.

Contribution

It introduces novel construction methods using partial antiflag collections of tactical configurations to generate directed strongly regular graphs.

Findings

Constructed new infinite families of directed strongly regular graphs

Methods can produce many nonisomorphic graphs with identical parameters

Extended previous work on graphs from partial geometries and group divisible designs

Abstract

This is the second report of our work on the construction of directed strongly regular graphs. In our previous work, we constructed a couple of infinite families of new directed strongly regular graphs on the sets of antiflags of partial geometries and group divisible designs. In this paper, we use some collections of antiflags (not the entire set of antiflags) of tactical configurations to construct another couple of infinite families of directed strongly regular graphs. Our construction methods are capable of producing many, if not all, nonisomorphic directed strongly regular graphs with same parameters.