A general method to find the spectrum and eigenspaces of the k-token graph of a cycle, and 2-token through continuous fractions

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. In this paper, we propose a general method to find the spectrum and eigenspaces of the k-token g...

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Authors: Reyes Quiróz, Mónica Andrea, Dalfó Simó, Cristina|||0000-0002-8438-9353, Messegué Buisan, Arnau|||0000-0002-7425-7592, Fiol Mora, Miquel Àngel|||0000-0003-1337-4952
Format: article
Publication Date:2024
Country:España
Institution:Universitat Politècnica de Catalunya (UPC)
Repository:UPCommons. Portal del coneixement obert de la UPC
Language:English
OAI Identifier:oai:upcommons.upc.edu:2117/419796
Online Access:https://hdl.handle.net/2117/419796
https://dx.doi.org/10.1016/j.dam.2024.09.031
Access Level:Open access
Keyword:Token graph
Laplacian spectrum
Lift graph
Over-lift graph
Continuous fraction
Àrees temàtiques de la UPC::Matemàtiques i estadística
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spelling A general method to find the spectrum and eigenspaces of the k-token graph of a cycle, and 2-token through continuous fractionsReyes Quiróz, Mónica AndreaDalfó Simó, Cristina|||0000-0002-8438-9353Messegué Buisan, Arnau|||0000-0002-7425-7592Fiol Mora, Miquel Àngel|||0000-0003-1337-4952Token graphLaplacian spectrumLift graphOver-lift graphContinuous fractionÀrees temàtiques de la UPC::Matemàtiques i estadísticaThe 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. In this paper, we propose a general method to find the spectrum and eigenspaces of the k-token graph Fk(Cn) of a cycle Cn. The method is based on the theory of lift graphs and the recently introduced theory of over-lifts. In the case of k = 2, we use continuous fractions to derive the spectrum and eigenspaces of the 2-token graph of Cn.This research has been supported by AGAUR, Catalonia from the Catalan Government under project 2021SGR00434 and MICINN, Spain 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, Catalonia with references AGRUPS-2022 and AGRUPS-2023.Peer ReviewedElsevier20252025-01-0120242024-12-03journal articlehttp://purl.org/coar/resource_type/c_6501VoRhttp://purl.org/coar/version/c_970fb48d4fbd8a85info:eu-repo/semantics/articleapplication/pdfhttps://hdl.handle.net/2117/419796https://dx.doi.org/10.1016/j.dam.2024.09.031reponame:UPCommons. Portal del coneixement obert de la UPCinstname:Universitat Politècnica de Catalunya (UPC)Inglésengopen accesshttp://purl.org/coar/access_right/c_abf2Attribution-NonCommercial-NoDerivatives 4.0 Internationalhttp://creativecommons.org/licenses/by-nc-nd/4.0/info:eu-repo/semantics/openAccessoai:upcommons.upc.edu:2117/4197962026-05-27T15:37:01Z
dc.title.none.fl_str_mv A general method to find the spectrum and eigenspaces of the k-token graph of a cycle, and 2-token through continuous fractions
title A general method to find the spectrum and eigenspaces of the k-token graph of a cycle, and 2-token through continuous fractions
spellingShingle A general method to find the spectrum and eigenspaces of the k-token graph of a cycle, and 2-token through continuous fractions
Reyes Quiróz, Mónica Andrea
Token graph
Laplacian spectrum
Lift graph
Over-lift graph
Continuous fraction
Àrees temàtiques de la UPC::Matemàtiques i estadística
title_short A general method to find the spectrum and eigenspaces of the k-token graph of a cycle, and 2-token through continuous fractions
title_full A general method to find the spectrum and eigenspaces of the k-token graph of a cycle, and 2-token through continuous fractions
title_fullStr A general method to find the spectrum and eigenspaces of the k-token graph of a cycle, and 2-token through continuous fractions
title_full_unstemmed A general method to find the spectrum and eigenspaces of the k-token graph of a cycle, and 2-token through continuous fractions
title_sort A general method to find the spectrum and eigenspaces of the k-token graph of a cycle, and 2-token through continuous fractions
dc.creator.none.fl_str_mv Reyes Quiróz, Mónica Andrea
Dalfó Simó, Cristina|||0000-0002-8438-9353
Messegué Buisan, Arnau|||0000-0002-7425-7592
Fiol Mora, Miquel Àngel|||0000-0003-1337-4952
author Reyes Quiróz, Mónica Andrea
author_facet Reyes Quiróz, Mónica Andrea
Dalfó Simó, Cristina|||0000-0002-8438-9353
Messegué Buisan, Arnau|||0000-0002-7425-7592
Fiol Mora, Miquel Àngel|||0000-0003-1337-4952
author_role author
author2 Dalfó Simó, Cristina|||0000-0002-8438-9353
Messegué Buisan, Arnau|||0000-0002-7425-7592
Fiol Mora, Miquel Àngel|||0000-0003-1337-4952
author2_role author
author
author
dc.subject.none.fl_str_mv Token graph
Laplacian spectrum
Lift graph
Over-lift graph
Continuous fraction
Àrees temàtiques de la UPC::Matemàtiques i estadística
topic Token graph
Laplacian spectrum
Lift graph
Over-lift graph
Continuous fraction
Àrees temàtiques de la UPC::Matemàtiques i estadística
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. In this paper, we propose a general method to find the spectrum and eigenspaces of the k-token graph Fk(Cn) of a cycle Cn. The method is based on the theory of lift graphs and the recently introduced theory of over-lifts. In the case of k = 2, we use continuous fractions to derive the spectrum and eigenspaces of the 2-token graph of Cn.
publishDate 2024
dc.date.none.fl_str_mv 2024
2024-12-03
2025
2025-01-01
dc.type.none.fl_str_mv journal article
http://purl.org/coar/resource_type/c_6501
VoR
http://purl.org/coar/version/c_970fb48d4fbd8a85
dc.type.openaire.fl_str_mv info:eu-repo/semantics/article
format article
dc.identifier.none.fl_str_mv https://hdl.handle.net/2117/419796
https://dx.doi.org/10.1016/j.dam.2024.09.031
url https://hdl.handle.net/2117/419796
https://dx.doi.org/10.1016/j.dam.2024.09.031
dc.language.none.fl_str_mv Inglés
eng
language_invalid_str_mv Inglés
language eng
dc.rights.none.fl_str_mv open access
http://purl.org/coar/access_right/c_abf2
Attribution-NonCommercial-NoDerivatives 4.0 International
http://creativecommons.org/licenses/by-nc-nd/4.0/
dc.rights.openaire.fl_str_mv info:eu-repo/semantics/openAccess
rights_invalid_str_mv open access
http://purl.org/coar/access_right/c_abf2
Attribution-NonCommercial-NoDerivatives 4.0 International
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:UPCommons. Portal del coneixement obert de la UPC
instname:Universitat Politècnica de Catalunya (UPC)
instname_str Universitat Politècnica de Catalunya (UPC)
reponame_str UPCommons. Portal del coneixement obert de la UPC
collection UPCommons. Portal del coneixement obert de la UPC
repository.name.fl_str_mv
repository.mail.fl_str_mv
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score 15,812455

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