Show simple item record

dc.contributor.authorDalfó, Cristina
dc.contributor.authorFiol, Miguel Angel
dc.date.accessioned2020-03-24T10:13:19Z
dc.date.issued2020
dc.identifier.issn0024-3795
dc.identifier.urihttp://hdl.handle.net/10459.1/68317
dc.description.abstractIn this paper, we present a method to obtain regular (or equitable) partitions of Cayley (di)graphs (that is, graphs, digraphs, or mixed graphs) of permutation groups on n letters. We prove that every partition of the number n gives rise to a regular partition of the Cayley graph. By using representation theory, we also obtain the complete spectra and the eigenspaces of the corresponding quotient (di)graphs. More precisely, we provide a method to find all the eigenvalues and eigenvectors of such (di)graphs, based on their irreducible representations. As examples, we apply this method to the pancake graphs P(n) and to a recent known family of mixed graphs Γ(d, n, r) (having edges with and without direction). As a byproduct, the existence of perfect codes s in P(n) allows us to give a lower bound for the multiplicity of its eigenvalue −1.
dc.description.sponsorshipThis research has been partially supported by AGAUR from the Catalan Government under project 2017SGR1087 and by MICINN from the Spanish Government under project PGC2018-095471-B-I00. The research of the first author has also been supported by MICINN from the Spanish Government under project MTM2017-83271-R. The research of the first author has also received funding from the European Union's Horizon 2020 research and innovation programme under the Marie Skłodowska-Curie grant agreement No 734922.
dc.format.mimetypeapplication/pdf
dc.language.isoeng
dc.publisherElsevier
dc.relationMINECO/PN2013-2016/PGC2018-095471-B-I00
dc.relationMINECO/PN2013-2016/MTM2017-83271-R
dc.relation.isformatofVersió postprint del document publicat a: https://doi.org/10.1016/j.laa.2020.03.015
dc.relation.ispartofLinear Algebra and its Applications, 2020, vol. 597, p. 94-112
dc.rightscc-by-nc-nd (c) Elsevier, 2020
dc.rights.urihttp://creativecommons.org/licenses/by-nc-nd/4.0/
dc.subjectLifted (di)graph
dc.subjectRegular partition
dc.subjectSpectrum
dc.titleSpectra and eigenspaces from regular partitions of Cayley (di)graphs of permutation groups
dc.typeinfo:eu-repo/semantics/article
dc.date.updated2020-03-24T10:13:19Z
dc.identifier.idgrec029891
dc.type.versioninfo:eu-repo/semantics/acceptedVersion
dc.rights.accessRightsinfo:eu-repo/semantics/embargoedAccess
dc.identifier.doihttps://doi.org/10.1016/j.laa.2020.03.015
dc.relation.projectIDinfo:eu-repo/grantAgreement/EC/H2020/734922/EU/CONNECT
dc.date.embargoEndDate2022-12-31


Files in this item

Thumbnail
Thumbnail
Thumbnail
Thumbnail

This item appears in the following Collection(s)

Show simple item record

cc-by-nc-nd (c) Elsevier, 2020
Except where otherwise noted, this item's license is described as cc-by-nc-nd (c) Elsevier, 2020