Generalised dual Seidel switching and Deza graphs with strongly regular children

TL;DR

This paper introduces a general approach to dual Seidel switching and explores Deza graphs with children that are strongly regular, expanding understanding of their structural properties and relationships.

Contribution

It presents a novel general method for dual Seidel switching and analyzes Deza graphs with strongly regular children, a new perspective in graph theory.

Findings

Developed a general approach to dual Seidel switching

Characterized Deza graphs with strongly regular children

Extended the theory of Deza graphs and their transformations

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 G_A and G_B of a Deza graph G are defined on the vertex set of G such that every two distinct vertices are adjacent in G_A or G_B 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.