On the spectra of token graphs of cycles and other graphs

The k-token graph Fk(G) of a graph G is the graph whose vertices are the k-subsets of vertices from G, two of which being adjacent whenever their symmetric difference is a pair of adjacent vertices in G. It is a known result that the algebraic connectivity (or second Laplacian eigenvalue) of Fk(G) e...

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Authors: Reyes, Mónica Andrea, Dalfó, Cristina, Fiol Mora, Miguel Ángel, Messegué, Arnau
Format: article
Status:Published version
Publication Date:2023
Country:España
Institution:Universitat de Lleida (UdL)
Repository:Repositori Obert UdL
OAI Identifier:oai:repositori.udl.cat:10459.1/464086
Online Access:https://doi.org/10.1016/j.laa.2023.09.004
https://hdl.handle.net/10459.1/464086
Access Level:Open access
Keyword:Algebraic connectivity
Binomial matrix
Laplacian spectrum
Lift graph
Regular partition
Token graph
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spelling On the spectra of token graphs of cycles and other graphsReyes, Mónica AndreaDalfó, CristinaFiol Mora, Miguel ÁngelMessegué, ArnauAlgebraic connectivityBinomial matrixLaplacian spectrumLift graphRegular partitionToken graphThe k-token graph Fk(G) of a graph G is the graph whose vertices are the k-subsets of vertices from G, two of which being adjacent whenever their symmetric difference is a pair of adjacent vertices in G. It is a known result that the algebraic connectivity (or second Laplacian eigenvalue) of Fk(G) equals the algebraic connectivity of G. In this paper, we first give results that relate the algebraic connectivities of a token graph and the same graph after removing a vertex. Then, we prove the result on the algebraic connectivity of 2-token graphs for two infinite families: the odd graphs Or for all r, and the multipartite complete graphs Kn for all n1,n2,…,nr In the case of cycles, we present a new method that allows us to compute the whole spectrum of F2(Cn). This method also allows us to obtain closed formulas that give asymptotically exact approximations for most of the eigenvalues of F2(Cn).This research has been supported by AGAUR from the Catalan Government under project 2021SGR00434 and MICINN from the Spanish Government under project PID2020-115442RB-I00. The research of M. A. Fiol was also supported by a grant from the Universitat Politècnica de Catalunya with references AGRUPS-2022 and AGRUPS-2023.Elsevier2023info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttps://doi.org/10.1016/j.laa.2023.09.004https://hdl.handle.net/10459.1/464086reponame: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/PID2020-115442RB-I00Reproducció del document publicat a https://doi.org/10.1016/j.laa.2023.09.004Linear Algebra and its Applications, vol. 679, p. 38-66cc-by-nc-nd (c) Reyes et al., 2023Attribution-NonCommercial-NoDerivatives 4.0 Internationalinfo:eu-repo/semantics/openAccesshttp://creativecommons.org/licenses/by-nc-nd/4.0/oai:repositori.udl.cat:10459.1/4640862026-06-24T12:42:17Z
dc.title.none.fl_str_mv On the spectra of token graphs of cycles and other graphs
title On the spectra of token graphs of cycles and other graphs
spellingShingle On the spectra of token graphs of cycles and other graphs
Reyes, Mónica Andrea
Algebraic connectivity
Binomial matrix
Laplacian spectrum
Lift graph
Regular partition
Token graph
title_short On the spectra of token graphs of cycles and other graphs
title_full On the spectra of token graphs of cycles and other graphs
title_fullStr On the spectra of token graphs of cycles and other graphs
title_full_unstemmed On the spectra of token graphs of cycles and other graphs
title_sort On the spectra of token graphs of cycles and other graphs
dc.creator.none.fl_str_mv Reyes, Mónica Andrea
Dalfó, Cristina
Fiol Mora, Miguel Ángel
Messegué, Arnau
author Reyes, Mónica Andrea
author_facet Reyes, Mónica Andrea
Dalfó, Cristina
Fiol Mora, Miguel Ángel
Messegué, Arnau
author_role author
author2 Dalfó, Cristina
Fiol Mora, Miguel Ángel
Messegué, Arnau
author2_role author
author
author
dc.subject.none.fl_str_mv Algebraic connectivity
Binomial matrix
Laplacian spectrum
Lift graph
Regular partition
Token graph
topic Algebraic connectivity
Binomial matrix
Laplacian spectrum
Lift graph
Regular partition
Token graph
description The k-token graph Fk(G) of a graph G is the graph whose vertices are the k-subsets of vertices from G, two of which being adjacent whenever their symmetric difference is a pair of adjacent vertices in G. It is a known result that the algebraic connectivity (or second Laplacian eigenvalue) of Fk(G) equals the algebraic connectivity of G. In this paper, we first give results that relate the algebraic connectivities of a token graph and the same graph after removing a vertex. Then, we prove the result on the algebraic connectivity of 2-token graphs for two infinite families: the odd graphs Or for all r, and the multipartite complete graphs Kn for all n1,n2,…,nr In the case of cycles, we present a new method that allows us to compute the whole spectrum of F2(Cn). This method also allows us to obtain closed formulas that give asymptotically exact approximations for most of the eigenvalues of F2(Cn).
publishDate 2023
dc.date.none.fl_str_mv 2023
dc.type.none.fl_str_mv info:eu-repo/semantics/article
info:eu-repo/semantics/publishedVersion
format article
status_str publishedVersion
dc.identifier.none.fl_str_mv https://doi.org/10.1016/j.laa.2023.09.004
https://hdl.handle.net/10459.1/464086
url https://doi.org/10.1016/j.laa.2023.09.004
https://hdl.handle.net/10459.1/464086
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/PID2020-115442RB-I00
Reproducció del document publicat a https://doi.org/10.1016/j.laa.2023.09.004
Linear Algebra and its Applications, vol. 679, p. 38-66
dc.rights.none.fl_str_mv cc-by-nc-nd (c) Reyes et al., 2023
Attribution-NonCommercial-NoDerivatives 4.0 International
info:eu-repo/semantics/openAccess
http://creativecommons.org/licenses/by-nc-nd/4.0/
rights_invalid_str_mv cc-by-nc-nd (c) Reyes et al., 2023
Attribution-NonCommercial-NoDerivatives 4.0 International
http://creativecommons.org/licenses/by-nc-nd/4.0/
eu_rights_str_mv openAccess
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
repository.name.fl_str_mv
repository.mail.fl_str_mv
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