Switched graphs of some strongly regular graphs related to the symplectic graph

TL;DR

This paper constructs new infinite families of strongly regular graphs related to symplectic graphs using a switching method, with geometric and coding theory interpretations, expanding the known classes of such graphs.

Contribution

It introduces a novel construction of strongly regular graphs based on symplectic graph geometry and switching techniques, providing explicit parameters and associated binary codes.

Findings

New infinite families of strongly regular graphs with specific parameters

Construction described via geometry of quadrics in projective space

Binary linear codes associated with the graphs have specified parameters

Abstract

Applying a method of Godsil and McKay \cite{GM} to some graphs related to the symplectic graph, a series of new infinite families of strongly regular graphs with parameters $(2^n\pm2^{(n-1)/2},2^{n-1}\pm2^{(n-1)/2},2^{n-2}\pm2^{(n-3)/2},2^{n-2}\pm2^{(n-1)/2})$ are constructed for any odd $n \geq 5$. The construction is described in terms of geometry of quadric in projective space. The binary linear codes of the switched graphs are $[2^n \mp 2^{\frac{n-1}{2}},n+3,2^{t+1}]_2$-code or $[2^n \mp 2^{\frac{n-1}{2}},n+3,2^{t+2}]_2$-code.