A general method to obtain the spectrum and local spectra of a graph from its regular partitions
Rights accessOpen Access
All rights reserved. This work is protected by the corresponding intellectual and industrial property rights. Without prejudice to any existing legal exemptions, reproduction, distribution, public communication or transformation of this work are prohibited without permission of the copyright holder
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, a method that gives all the spectrum, and also the local spectra, of a graph from the quotient matrices of some of its regular partitions, is proposed. Moreover, from such partitions, the C -local multiplicities of any class of vertices C is also determined, and some applications of these parameters in the characterization of completely regular codes and their inner distributions are described. As examples, it is shown how to find the eigenvalues and (local) multiplicities of walk-regular, distance-regular, and distance-biregular graphs.
CitationDalfo, C.; Fiol, M. A general method to obtain the spectrum and local spectra of a graph from its regular partitions. "Electronic journal of linear algebra", 12 Juliol 2020, vol. 36, núm. 36, p. 446-460.