A general method to obtain the spectrum and local spectra of a graph from its regular partitions

2019/01/23 by Dalfó, C., Fiol, M. A. · 1 citation
#05C50 #05E30 #Combinatorics (math.CO) #FOS: Mathematics

paper · doi:10.48550/arxiv.1901.08048

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 Γ 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.

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