New construction of strongly regular graphs with parameters of the complement of symplectic graph

Vladislav V. Kabanov

Published 2022-03-08Version 1

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 present a new prolific construction of strongly regular graphs with parameters of the complement of symplectic graph using a new prolific construction of one type of divisible design graphs.