# Spectra and eigenspaces of arbitrary lifts of graphs

## TL;DR

This paper presents a detailed method for explicitly determining the spectra and eigenspaces of arbitrary graph lifts, regardless of regularity, enhancing understanding of their spectral properties.

## Contribution

It introduces a novel explicit approach for analyzing spectra and eigenspaces of arbitrary graph lifts, extending previous methods limited to specific cases.

## Key findings

- Provides a comprehensive method for spectral analysis of graph lifts
- Enables explicit computation of eigenspaces for arbitrary lifts
- Applicable to both regular and irregular graph lifts

## Abstract

We describe, in a very explicit way, a method for determining the spectra and bases of all the corresponding eigenspaces of arbitrary lifts of graphs (regular or not).