Spectra and eigenspaces from regular partitions of Cayley (di)graphs of permutation groups

In 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 represent...

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Detalles Bibliográficos
Autores: Dalfó, Cristina, Fiol Mora, Miguel Ángel
Tipo de recurso: artículo
Estado:Versión aceptada para publicación
Fecha de publicación:2020
País:España
Institución:Universitat de Lleida (UdL)
Repositorio:Repositori Obert UdL
OAI Identifier:oai:repositori.udl.cat:10459.1/68317
Acceso en línea:https://doi.org/10.1016/j.laa.2020.03.015
http://hdl.handle.net/10459.1/68317
Access Level:acceso abierto
Palabra clave:Lifted (di)graph
Regular partition
Spectrum
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spelling Spectra and eigenspaces from regular partitions of Cayley (di)graphs of permutation groupsDalfó, CristinaFiol Mora, Miguel ÁngelLifted (di)graphRegular partitionSpectrumIn 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.This 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.Elsevier2020info:eu-repo/semantics/articleinfo:eu-repo/semantics/acceptedVersionapplication/pdfhttps://doi.org/10.1016/j.laa.2020.03.015http://hdl.handle.net/10459.1/68317reponame:Repositori Obert UdL instname:Universitat de Lleida (UdL)Inglésinfo:eu-repo/grantAgreement/AEI/Plan Estatal de Investigación Científica y Técnica y de Innovación 2017-2020/PGC2018-095471-B-I00info:eu-repo/grantAgreement/AEI/Plan Estatal de Investigación Científica y Técnica y de Innovación 2013-2016/MTM2017-83271-RVersió postprint del document publicat a: https://doi.org/10.1016/j.laa.2020.03.015Linear Algebra and its Applications, 2020, vol. 597, p. 94-112info:eu-repo/grantAgreement/EC/H2020/734922cc-by-nc-nd (c) Elsevier, 2020info:eu-repo/semantics/openAccesshttp://creativecommons.org/licenses/by-nc-nd/4.0/oai:repositori.udl.cat:10459.1/683172026-06-24T12:42:17Z
dc.title.none.fl_str_mv Spectra and eigenspaces from regular partitions of Cayley (di)graphs of permutation groups
title Spectra and eigenspaces from regular partitions of Cayley (di)graphs of permutation groups
spellingShingle Spectra and eigenspaces from regular partitions of Cayley (di)graphs of permutation groups
Dalfó, Cristina
Lifted (di)graph
Regular partition
Spectrum
title_short Spectra and eigenspaces from regular partitions of Cayley (di)graphs of permutation groups
title_full Spectra and eigenspaces from regular partitions of Cayley (di)graphs of permutation groups
title_fullStr Spectra and eigenspaces from regular partitions of Cayley (di)graphs of permutation groups
title_full_unstemmed Spectra and eigenspaces from regular partitions of Cayley (di)graphs of permutation groups
title_sort Spectra and eigenspaces from regular partitions of Cayley (di)graphs of permutation groups
dc.creator.none.fl_str_mv Dalfó, Cristina
Fiol Mora, Miguel Ángel
author Dalfó, Cristina
author_facet Dalfó, Cristina
Fiol Mora, Miguel Ángel
author_role author
author2 Fiol Mora, Miguel Ángel
author2_role author
dc.subject.none.fl_str_mv Lifted (di)graph
Regular partition
Spectrum
topic Lifted (di)graph
Regular partition
Spectrum
description In 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.
publishDate 2020
dc.date.none.fl_str_mv 2020
dc.type.none.fl_str_mv info:eu-repo/semantics/article
info:eu-repo/semantics/acceptedVersion
format article
status_str acceptedVersion
dc.identifier.none.fl_str_mv https://doi.org/10.1016/j.laa.2020.03.015
http://hdl.handle.net/10459.1/68317
url https://doi.org/10.1016/j.laa.2020.03.015
http://hdl.handle.net/10459.1/68317
dc.language.none.fl_str_mv Inglés
language_invalid_str_mv Inglés
dc.relation.none.fl_str_mv info:eu-repo/grantAgreement/AEI/Plan Estatal de Investigación Científica y Técnica y de Innovación 2017-2020/PGC2018-095471-B-I00
info:eu-repo/grantAgreement/AEI/Plan Estatal de Investigación Científica y Técnica y de Innovación 2013-2016/MTM2017-83271-R
Versió postprint del document publicat a: https://doi.org/10.1016/j.laa.2020.03.015
Linear Algebra and its Applications, 2020, vol. 597, p. 94-112
info:eu-repo/grantAgreement/EC/H2020/734922
dc.rights.none.fl_str_mv cc-by-nc-nd (c) Elsevier, 2020
info:eu-repo/semantics/openAccess
http://creativecommons.org/licenses/by-nc-nd/4.0/
rights_invalid_str_mv cc-by-nc-nd (c) Elsevier, 2020
http://creativecommons.org/licenses/by-nc-nd/4.0/
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv application/pdf
dc.publisher.none.fl_str_mv Elsevier
publisher.none.fl_str_mv Elsevier
dc.source.none.fl_str_mv reponame:Repositori Obert UdL
instname:Universitat de Lleida (UdL)
instname_str Universitat de Lleida (UdL)
reponame_str Repositori Obert UdL
collection Repositori Obert UdL
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