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

dc.contributor.authorDalfó, Cristina
dc.contributor.authorFiol Mora, Miguel Ángel
dc.date.accessioned2020-12-21T09:10:14Z
dc.date.available2020-12-21T09:10:14Z
dc.date.issued2020-07-12
dc.date.updated2020-12-21T09:10:14Z
dc.description.abstractIt 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.
dc.description.sponsorshipPartially supported by AGAUR from the Catalan Government under project 2017SGR1087 and by MICINN from the Spanish Governmentunder projects PGC2018-095471-B-I00 and MTM2017-83271-R. Also received funding from the European Union’s Horizon 2020 research and innovation programme under the Marie Sk lodowska-Curie grant agreement no. 734922
dc.format.mimetypeapplication/pdf
dc.identifier.doihttps://doi.org/10.13001/ela.2020.5225
dc.identifier.idgrec030376
dc.identifier.issn1081-3810
dc.identifier.urihttp://hdl.handle.net/10459.1/70126
dc.language.isoeng
dc.publisherInternational Linear Algebra Society
dc.relationinfo:eu-repo/grantAgreement/AEI/Plan Estatal de Investigación Científica y Técnica y de Innovación 2017-2020/PGC2018-095471-B-I00/ES/ESTUDIO MATEMATICO DE LOS FALLOS EN CASCADA EN SISTEMAS COMPLEJOS MEDIANTE INVARIANTES Y CENTRALIDADES EN GRAFOS. APLICACIONES A REDES REALES/
dc.relationinfo:eu-repo/grantAgreement/AEI/Plan Estatal de Investigación Científica y Técnica y de Innovación 2013-2016/MTM2017-83271-R/ES/CRIPTOGRAFIA Y CODIGOS PARA APLICACIONES SEGURAS Y FIABLES/
dc.relation.isformatofVersió postprint del document publicat a: https://doi.org/10.13001/ela.2020.5225
dc.relation.ispartofElectronic Journal Of Linear Algebra, 2020, vol. 36, num. 36, p. 446-460
dc.relation.projectIDinfo:eu-repo/grantAgreement/EC/H2020/734922/EU/CONNECT
dc.rights(c) Dalfó i Fiol, 2020
dc.rights.accessRightsinfo:eu-repo/semantics/openAccess
dc.subjectAdjacency matrix
dc.subjectSpectrum
dc.subjectEigenvalues
dc.subjectLocal multiplicities
dc.subjectWalk-regular graph
dc.subjectC-local spectrum
dc.subjectCompletely regular code
dc.titleA general method to obtain the spectrum and local spectra of a graph from its regular partitions
dc.typeinfo:eu-repo/semantics/article
dc.type.versionaccepted/Version
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