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

Dalfó, Cristina; Fiol, Miguel Angel

doi:https://doi.org/10.13001/ela.2020.5225

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Issue date

2020-07-12

Author

Dalfó, Cristina

Fiol, Miguel Angel

Suggested citation

Dalfó, Cristina; Fiol, Miguel Angel; . (2020) . A general method to obtain the spectrum and local spectra of a graph from its regular partitions. Electronic Journal Of Linear Algebra, 2020, vol. 36, num. 36, p. 446-460. https://doi.org/10.13001/ela.2020.5225.

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, 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.

URI

http://hdl.handle.net/10459.1/70126

DOI

https://doi.org/10.13001/ela.2020.5225

Is part of

Electronic Journal Of Linear Algebra, 2020, vol. 36, num. 36, p. 446-460