On the spectra and eigenspaces of the universal adjacency matrices of arbitrary lifts of graphs

The universal adjacency matrix U of a graph Γ, with adjacency matrix A, is a linear combination of A, the diagonal matrix D of vertex degrees, the identity matrix I, and the all-1 matrix J with real coefficients, that is, U=c1A+c2D+c3I+c4J, with ci∈R and c1≠0. Thus, in particular cases, U may be the...

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Autores: Dalfó, Cristina, Fiol Mora, Miguel Ángel, Pavlíková, Sona, Sirán, Jozef
Formato: artículo
Estado:Versión aceptada para publicación
Fecha de publicación:2022
País:España
Recursos:Varias* (Consorci de Biblioteques Universitáries de Catalunya, Centre de Serveis Científics i Acadèmics de Catalunya)
Repositorio:Recercat. Dipósit de la Recerca de Catalunya
OAI Identifier:oai:recercat.cat:10459.1/83176
Acesso em linha:https://doi.org/10.1080/03081087.2022.2042174
http://hdl.handle.net/10459.1/83176
Access Level:acceso abierto
Palavra-chave:Graph
Lift
Universal adjacency matrix
Eigenspace
Symmetric square
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spelling On the spectra and eigenspaces of the universal adjacency matrices of arbitrary lifts of graphsDalfó, CristinaFiol Mora, Miguel ÁngelPavlíková, SonaSirán, JozefGraphLiftUniversal adjacency matrixEigenspaceSymmetric squareThe universal adjacency matrix U of a graph Γ, with adjacency matrix A, is a linear combination of A, the diagonal matrix D of vertex degrees, the identity matrix I, and the all-1 matrix J with real coefficients, that is, U=c1A+c2D+c3I+c4J, with ci∈R and c1≠0. Thus, in particular cases, U may be the adjacency matrix, the Laplacian, the signless Laplacian, and the Seidel matrix. In this paper, we develop a method for determining the universal spectra and bases of all the corresponding eigenspaces of arbitrary lifts of graphs (regular or not). As an example, the method is applied to give an efficient algorithm to determine the characteristic polynomial of the Laplacian matrix of the symmetric squares of odd cycles, together with closed formulas for some of their eigenvalues.The first author has received funding from the European Union’s Horizon 2020 research and innovation programme under the Marie Sk lodowska-Curie grant agreement No 734922. The research of the two first authors is 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 third and fourth authors acknowledge support from the APVV Research Grants 15-0220 and 17-0428, and the VEGA Research Grants 1/0142/17 and 1/0238/19.Taylor & Francis2022info:eu-repo/semantics/articleinfo:eu-repo/semantics/acceptedVersionapplication/pdfhttps://doi.org/10.1080/03081087.2022.2042174http://hdl.handle.net/10459.1/83176reponame:Recercat. Dipósit de la Recerca de Catalunyainstname:Varias* (Consorci de Biblioteques Universitáries de Catalunya, Centre de Serveis Científics i Acadèmics de Catalunya)Inglésinfo:eu-repo/grantAgreement/AEI/Plan Estatal de Investigación Científica y Técnica y de Innovación 2013-2016/MTM2017-83271-Rinfo:eu-repo/grantAgreement/AEI/Plan Estatal de Investigación Científica y Técnica y de Innovación 2017-2020/PGC2018-095471-B-I00Versió postprint del document publicat a: https://doi.org/10.1080/03081087.2022.2042174Linear and Multilinear Algebra, 2022, vol. 71, núm. 5, p. 693–710info:eu-repo/grantAgreement/EC/H2020/734922(c) Taylor & Francis, 2022info:eu-repo/semantics/openAccessoai:recercat.cat:10459.1/831762026-05-29T05:05:01Z
dc.title.none.fl_str_mv On the spectra and eigenspaces of the universal adjacency matrices of arbitrary lifts of graphs
title On the spectra and eigenspaces of the universal adjacency matrices of arbitrary lifts of graphs
spellingShingle On the spectra and eigenspaces of the universal adjacency matrices of arbitrary lifts of graphs
Dalfó, Cristina
Graph
Lift
Universal adjacency matrix
Eigenspace
Symmetric square
title_short On the spectra and eigenspaces of the universal adjacency matrices of arbitrary lifts of graphs
title_full On the spectra and eigenspaces of the universal adjacency matrices of arbitrary lifts of graphs
title_fullStr On the spectra and eigenspaces of the universal adjacency matrices of arbitrary lifts of graphs
title_full_unstemmed On the spectra and eigenspaces of the universal adjacency matrices of arbitrary lifts of graphs
title_sort On the spectra and eigenspaces of the universal adjacency matrices of arbitrary lifts of graphs
dc.creator.none.fl_str_mv Dalfó, Cristina
Fiol Mora, Miguel Ángel
Pavlíková, Sona
Sirán, Jozef
author Dalfó, Cristina
author_facet Dalfó, Cristina
Fiol Mora, Miguel Ángel
Pavlíková, Sona
Sirán, Jozef
author_role author
author2 Fiol Mora, Miguel Ángel
Pavlíková, Sona
Sirán, Jozef
author2_role author
author
author
dc.subject.none.fl_str_mv Graph
Lift
Universal adjacency matrix
Eigenspace
Symmetric square
topic Graph
Lift
Universal adjacency matrix
Eigenspace
Symmetric square
description The universal adjacency matrix U of a graph Γ, with adjacency matrix A, is a linear combination of A, the diagonal matrix D of vertex degrees, the identity matrix I, and the all-1 matrix J with real coefficients, that is, U=c1A+c2D+c3I+c4J, with ci∈R and c1≠0. Thus, in particular cases, U may be the adjacency matrix, the Laplacian, the signless Laplacian, and the Seidel matrix. In this paper, we develop a method for determining the universal spectra and bases of all the corresponding eigenspaces of arbitrary lifts of graphs (regular or not). As an example, the method is applied to give an efficient algorithm to determine the characteristic polynomial of the Laplacian matrix of the symmetric squares of odd cycles, together with closed formulas for some of their eigenvalues.
publishDate 2022
dc.date.none.fl_str_mv 2022
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/10.1080/03081087.2022.2042174
http://hdl.handle.net/10459.1/83176
url https://doi.org/10.1080/03081087.2022.2042174
http://hdl.handle.net/10459.1/83176
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 2013-2016/MTM2017-83271-R
info:eu-repo/grantAgreement/AEI/Plan Estatal de Investigación Científica y Técnica y de Innovación 2017-2020/PGC2018-095471-B-I00
Versió postprint del document publicat a: https://doi.org/10.1080/03081087.2022.2042174
Linear and Multilinear Algebra, 2022, vol. 71, núm. 5, p. 693–710
info:eu-repo/grantAgreement/EC/H2020/734922
dc.rights.none.fl_str_mv (c) Taylor & Francis, 2022
info:eu-repo/semantics/openAccess
rights_invalid_str_mv (c) Taylor & Francis, 2022
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv application/pdf
dc.publisher.none.fl_str_mv Taylor & Francis
publisher.none.fl_str_mv Taylor & Francis
dc.source.none.fl_str_mv reponame:Recercat. Dipósit de la Recerca de Catalunya
instname:Varias* (Consorci de Biblioteques Universitáries de Catalunya, Centre de Serveis Científics i Acadèmics de Catalunya)
instname_str Varias* (Consorci de Biblioteques Universitáries de Catalunya, Centre de Serveis Científics i Acadèmics de Catalunya)
reponame_str Recercat. Dipósit de la Recerca de Catalunya
collection Recercat. Dipósit de la Recerca de Catalunya
repository.name.fl_str_mv
repository.mail.fl_str_mv
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