A New Construction of Strongly Regular Graphs with Parameters of the Complement Symplectic Graph

Abstract

The symplectic graph $Sp(2d, q)$ is the collinearity graph of the symplectic space of dimension $2d$ over the 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.