Combined voltage assignments, factored lifts, and their spectra
Combinatorics
2024-09-05 v1
Abstract
We consider lifting eigenvalues and eigenvectors of graphs to their {\em factored lifts}, derived by means of a {\em combined voltage assignment} in a group. The latter extends the concept of (ordinary) voltage assignments known from regular coverings and corresponds to the cases of generalized covers of Poto\v{c}nik and Toledo (2021) in which a group of automorphisms of a lift acts freely on its arc set. With the help of group representations and certain matrices over complex group rings associated with the graphs to be lifted, we develop a method for the determination of the complete spectra of the factored lift graphs and derive a sufficient condition for lifting eigenvectors.
Cite
@article{arxiv.2409.02463,
title = {Combined voltage assignments, factored lifts, and their spectra},
author = {C. Dalfó and M. A. Fiol and S. Pavlíková and J. Širáň},
journal= {arXiv preprint arXiv:2409.02463},
year = {2024}
}