Strongly regular graphs with the same parameters as the symplectic graph

TL;DR

This paper constructs new families of strongly regular graphs with parameters matching the symplectic graph using automorphism groups and Godsil-McKay switching, demonstrating their non-isomorphism through neighbor analysis.

Contribution

It introduces four new families of strongly regular graphs with symplectic parameters, expanding known examples and applying novel switching techniques.

Findings

Four new strongly regular graph families found

Switched graphs are proven non-isomorphic

Includes a previously discovered graph by Abiad and Haemers

Abstract

We consider orbit partitions of groups of automorphisms for the symplectic graph and apply Godsil-McKay switching. As a result, we find four families of strongly regular graphs with the same parameters as the symplectic graphs, including the one discovered by Abiad and Haemers. Also, we prove that switched graphs are non-isomorphic to each other by considering the number of common neighbors of three vertices.