Design switching on graphs

TL;DR

This paper introduces a unified framework for graph switching methods derived from combinatorial designs, explaining existing techniques like GM and WQH switching and their ability to produce cospectral graphs.

Contribution

It presents a general approach based on (r, lambda)-designs to generate and understand various graph switching methods.

Findings

Unified framework for graph switching methods

Explanation of GM and WQH switching as special cases

Ability to produce cospectral graphs using design-based switching

Abstract

We show that each (r, lambda)-design yields a class of switching methods that can be used produce cospectral graphs. We use this to explain several specific switching methods such as Godsil-McKay (GM) switching and Wang-Qiu-Hu (WQH) switching.