Generic spectrum of the weighted Laplacian operator on Cayley graphs
Spectral Theory
2024-06-05 v3 Mathematical Physics
Combinatorics
math.MP
Abstract
In this paper, we investigate the spectrum of a class of weighted Laplacians on Cayley graphs and determine under what conditions the corresponding eigenspaces are generically irreducible. Specifically, we analyze the spectrum on left-invariant Cayley graphs endowed with an invariant metric, and we give some criteria for generically irreducible eigenspaces. Additionally, we introduce an operator that is comparable to the Laplacian and show that the same criterion holds.
Keywords
Cite
@article{arxiv.2009.07908,
title = {Generic spectrum of the weighted Laplacian operator on Cayley graphs},
author = {Cristian F. Coletti and Lucas R. de Lima and Diego S. de Oliveira and Marcus A. M. Marrocos},
journal= {arXiv preprint arXiv:2009.07908},
year = {2024}
}
Comments
18 pages, 2 figures; typos corrected