A Switching for all Strongly Regular Collinearity Graphs From Polar Spaces

TL;DR

This paper introduces a new construction method for strongly regular graphs derived from polar spaces, producing non-isomorphic graphs with identical parameters to collinearity graphs, many of which are novel.

Contribution

It presents a general construction of strongly regular graphs from polar spaces that yields new, non-isomorphic graphs with the same parameters as collinearity graphs.

Findings

Constructed new strongly regular graphs from polar spaces

Proved these graphs are non-isomorphic to collinearity graphs

Most of these graphs are new for given parameters

Abstract

We describe a general construction of strongly regular graphs from the collinearity graph of a finite classical polar spaces of rank at least $3$ over a finite field of order $q$. We show that these graphs are non-isomorphic to the collinearity graphs and have the same parameters. To our knowledge for most of these parameters these graphs are new as the collinearity graphs were the only known examples.