Generalised dual Seidel switching and Deza graphs with strongly regular children

Abstract

A Deza graph G with parameters (n,k,b,a) is a k-regular graph with n vertices such that any two distinct vertices have b or a common neighbours, where b⩾a. The children GA and GB of a Deza graph G are defined on the vertex set of G such that every two distinct vertices are adjacent in GA or GB if and only if they have a or b common neighbours, respectively. In this paper we present a general approach to dual Seidel switching and investigate Deza graphs whose children are strongly regular graphs.