A new construction of strongly regular graphs with parameters of the complement symplectic graph

TL;DR

This paper introduces a novel method to construct strongly regular graphs with parameters matching the complement of symplectic graphs, utilizing divisible design graphs to expand the class of known such graphs.

Contribution

It presents a new construction technique for strongly regular graphs based on divisible design graphs, specifically targeting parameters of the complement symplectic graph.

Findings

Constructed new strongly regular graphs with specific parameters

Extended the understanding of graph structures related to symplectic spaces

Provided a framework for generating graphs with desired regularity properties

Abstract

The symplectic graph Sp(2d, q) is the collinearity graph of the symplectic space of dimension 2d over a finite field of order q. A k-regular graph on v vertices is a divisible design graph with parameters (v, k, lambda_1, lambda_2 ,m,n) if its vertex set can be partitioned into m classes of size n, such that any two different vertices from the same class have lambda_1 common neighbours, and any two vertices from different classes have lambda_2 common neighbours whenever it is not complete or edgeless. In this paper we propose a new construction of strongly regular graphs with the parameters of the complement of the symplectic graph using divisible design graphs.