A switching method for constructing cospectral gain graphs

TL;DR

This paper introduces a novel switching method for constructing cospectral gain graphs, generalizing existing techniques and expanding the toolkit for analyzing spectral properties of gain graphs.

Contribution

The paper presents a new switching method for constructing cospectral gain graphs, extending previous methods and providing a broader framework for spectral graph analysis.

Findings

The new switching method can generate cospectral gain graphs.

Previous cospectrality methods are special cases of this new approach.

The method broadens the understanding of spectral properties in gain graphs.

Abstract

A gain graph over a group $G$, also referred to as $G$-gain graph, is a graph where an element of a group $G$, called gain, is assigned to each oriented edge, in such a way that the inverse element is associated with the opposite orientation. Gain graphs can be regarded as a generalization of signed graphs, among others. In this work, we show a new switching method to construct cospectral gain graphs. Some previous methods known for graph cospectrality follow as a corollary of our results.