Strongly regular graphs with parameters (81,30,9,12) and a new partial geometry pg(5,5,2)

TL;DR

This paper reports the discovery of twelve new strongly regular graphs with specific parameters, including a unique geometric graph that leads to a novel partial geometry, expanding the understanding of graph structures and their geometric counterparts.

Contribution

The paper introduces twelve new strongly regular graphs with parameters (81,30,9,12), including a unique geometric graph that defines a new partial geometry not isomorphic to known examples.

Findings

Twelve new strongly regular graphs with parameters (81,30,9,12) identified.

One graph is geometric, leading to a new partial geometry pg(5,5,2).

The new partial geometry is not isomorphic to the classical one by van Lint and Schrijver.

Abstract

Twelve new strongly regular graphs with parameters (81,30,9,12) are found as graphs invariant under certain subgroups of the automorphism groups of the two previously known graphs that arise from 2-weight codes. One of these new graphs is geometric and yields a partial geometry with parameters pg(5,5,2) that is not isomorphic to the partial geometry discovered by J. H. van Lint and A. Schrijver in 1981.