A general method to obtain the spectrum and local spectra of a graph from its regular partitions
Combinatorics
2019-01-24 v1
Abstract
It is well known that, in general, part of the spectrum of a graph can be obtained from the adjacency matrix of its quotient graph given by a regular partition. In this paper, we propose a method to obtain all the spectrum, and also the local spectra, of a graph from the quotient matrices of some of its regular partitions. As examples, it is shown how to find the eigenvalues and (local) multiplicities of walk-regular, distance-regular, and distance-biregular graphs.
Keywords
Cite
@article{arxiv.1901.08048,
title = {A general method to obtain the spectrum and local spectra of a graph from its regular partitions},
author = {C. Dalfó and M. A. Fiol},
journal= {arXiv preprint arXiv:1901.08048},
year = {2019}
}