A Switching for all Strongly Regular Collinearity Graphs From Polar Spaces

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.

arXiv comment11 pages, older version published in the Journal of Algebraic Combinatorics, fixed a typo in Lemma 3.5 and added a comment due to Kantor