Some bounds on the Laplacian eigenvalues of token graphs
The k-token graph Fk(G) of a graph G on n vertices is the graph whose vertices are the n k-subsets of vertices from G, two of which are adjacent whenever their symmetric difference is a pair of adjacent vertices in G. It is known that the algebraic connectivity (or second Laplacian eigen- value) of...
| Autores: | , , |
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| Tipo de recurso: | artículo |
| Estado: | Versión enviada para evaluación y publicación |
| Fecha de publicación: | 2025 |
| País: | España |
| Institución: | 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:10459.1/467299 |
| Acceso en línea: | https://doi.org/10.1016/j.disc.2024.114382 https://hdl.handle.net/10459.1/467299 |
| Access Level: | acceso abierto |
| Palabra clave: | Token graph Laplacian spectrum Algebraic connectivity Binomial matrix |
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Some bounds on the Laplacian eigenvalues of token graphsDalfó, CristinaFiol Mora, Miguel ÁngelMessegué, ArnauToken graphLaplacian spectrumAlgebraic connectivityBinomial matrixThe k-token graph Fk(G) of a graph G on n vertices is the graph whose vertices are the n k-subsets of vertices from G, two of which are adjacent whenever their symmetric difference is a pair of adjacent vertices in G. It is known that the algebraic connectivity (or second Laplacian eigen- value) of Fk(G) equals the algebraic connectivity α(G) of G. In this paper, we give some bounds on the (Laplacian) eigenvalues of the k-token graph (including the algebraic connectivity) in terms of the h-token graph, with h ≤ k. For instance, we prove that if λ is an eigenvalue of Fk(G), but not of G, then λ ≥ kα(G) − k + 1. As a consequence, we conclude that if α(G) ≥ k, then α(Fh(G)) = α(G) for every h ≤ k.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.Elsevier2025info:eu-repo/semantics/articleinfo:eu-repo/semantics/submittedVersionhttps://doi.org/10.1016/j.disc.2024.114382https://hdl.handle.net/10459.1/467299reponame: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 2017-2020/PID2020-115442RB-I00Versió preprint del document publicat a: doi.org/10.1016/j.disc.2024.114382Discrete Mathematics, 2025, vol.348, núm. 4, p.114382(c) Dalfó et al., 2025info:eu-repo/semantics/openAccessoai:recercat.cat:10459.1/4672992026-05-29T05:05:01Z |
| dc.title.none.fl_str_mv |
Some bounds on the Laplacian eigenvalues of token graphs |
| title |
Some bounds on the Laplacian eigenvalues of token graphs |
| spellingShingle |
Some bounds on the Laplacian eigenvalues of token graphs Dalfó, Cristina Token graph Laplacian spectrum Algebraic connectivity Binomial matrix |
| title_short |
Some bounds on the Laplacian eigenvalues of token graphs |
| title_full |
Some bounds on the Laplacian eigenvalues of token graphs |
| title_fullStr |
Some bounds on the Laplacian eigenvalues of token graphs |
| title_full_unstemmed |
Some bounds on the Laplacian eigenvalues of token graphs |
| title_sort |
Some bounds on the Laplacian eigenvalues of token graphs |
| dc.creator.none.fl_str_mv |
Dalfó, Cristina Fiol Mora, Miguel Ángel Messegué, Arnau |
| author |
Dalfó, Cristina |
| author_facet |
Dalfó, Cristina Fiol Mora, Miguel Ángel Messegué, Arnau |
| author_role |
author |
| author2 |
Fiol Mora, Miguel Ángel Messegué, Arnau |
| author2_role |
author author |
| dc.subject.none.fl_str_mv |
Token graph Laplacian spectrum Algebraic connectivity Binomial matrix |
| topic |
Token graph Laplacian spectrum Algebraic connectivity Binomial matrix |
| description |
The k-token graph Fk(G) of a graph G on n vertices is the graph whose vertices are the n k-subsets of vertices from G, two of which are adjacent whenever their symmetric difference is a pair of adjacent vertices in G. It is known that the algebraic connectivity (or second Laplacian eigen- value) of Fk(G) equals the algebraic connectivity α(G) of G. In this paper, we give some bounds on the (Laplacian) eigenvalues of the k-token graph (including the algebraic connectivity) in terms of the h-token graph, with h ≤ k. For instance, we prove that if λ is an eigenvalue of Fk(G), but not of G, then λ ≥ kα(G) − k + 1. As a consequence, we conclude that if α(G) ≥ k, then α(Fh(G)) = α(G) for every h ≤ k. |
| publishDate |
2025 |
| dc.date.none.fl_str_mv |
2025 |
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info:eu-repo/semantics/article info:eu-repo/semantics/submittedVersion |
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article |
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submittedVersion |
| dc.identifier.none.fl_str_mv |
https://doi.org/10.1016/j.disc.2024.114382 https://hdl.handle.net/10459.1/467299 |
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https://doi.org/10.1016/j.disc.2024.114382 https://hdl.handle.net/10459.1/467299 |
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Inglés |
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Inglés |
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info:eu-repo/grantAgreement/AEI/Plan Estatal de Investigación Científica y Técnica y de Innovación 2017-2020/PID2020-115442RB-I00 Versió preprint del document publicat a: doi.org/10.1016/j.disc.2024.114382 Discrete Mathematics, 2025, vol.348, núm. 4, p.114382 |
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(c) Dalfó et al., 2025 info:eu-repo/semantics/openAccess |
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(c) Dalfó et al., 2025 |
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openAccess |
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Elsevier |
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Elsevier |
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reponame:Recercat. Dipósit de la Recerca de Catalunya instname:Varias* (Consorci de Biblioteques Universitáries de Catalunya, Centre de Serveis Científics i Acadèmics de Catalunya) |
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Recercat. Dipósit de la Recerca de Catalunya |
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