Factored lifts of graphs and their spectra: the Abelian case

Abstract

In this paper, 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 all the eigenvalues and eigenspaces of factored lifts when the underlying group is Abelian.

The first two authors' research has been supported by AGAUR from the Catalan Government under project 2021SGR00434 and MICINN from the Spanish Government under project PID2020-115442RB-I00. The second author's research was also supported by a grant from the Universitat Politècnica de Catalunya, with reference AGRUPS-2024. The third and fourth authors acknowledge support of this research by the APVV Research Grants 22-0005 and 23-0076, and the VEGA Research Grants 1/0069/23 and 1/0011/25.