On factored lifts of graphs and their spectra

TL;DR

This paper introduces factored lifts of graphs, a generalization of lift graphs, along with a new method for calculating their eigenvalues and eigenspaces, enhancing spectral analysis techniques.

Contribution

It presents the concept of factored lifts and a novel approach for spectral computation, expanding the theoretical framework of graph lifts.

Findings

Defined the concept of factored lifts

Developed a new spectral computation method

Extended spectral analysis to generalized lifts

Abstract

In this note, we introduce the concept of factored lift, associated with a combined voltage graph, as a generalization of the lift graph. We present a new method for computing the eigenvalues and eigenspaces of factored lifts.