On the Laplacian spectra of token graphs
We study the Laplacian spectrum of token graphs, also called symmetric powers of 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. In this...
| Autores: | , , , , , , |
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| Formato: | artículo |
| Estado: | Versión publicada |
| Fecha de publicación: | 2021 |
| 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:10459.1/71777 |
| Acesso em linha: | https://doi.org/10.1016/j.laa.2021.05.005 http://hdl.handle.net/10459.1/71777 |
| Access Level: | acceso abierto |
| Palavra-chave: | Token graph Laplacian spectrum Algebraic connectivity Binomial matrix Adjacency spectrum |
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On the Laplacian spectra of token graphsDalfó, CristinaDuque, F.Fabila Monroy, R.Fiol Mora, Miguel ÁngelHuemer, ClemensZaragoza Martínez, F.J.Trujillo Negrete, A.L.Token graphLaplacian spectrumAlgebraic connectivityBinomial matrixAdjacency spectrumWe study the Laplacian spectrum of token graphs, also called symmetric powers of 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. In this paper, we give a relationship between the Laplacian spectra of any two token graphs of a given graph. In particular, we show that, for any integers h and k such that 1 ≤ h ≤ k ≤ n 2 , the Laplacian spectrum of Fh(G) is contained in the Laplacian spectrum of Fk(G). We also show that the doubled odd graphs and doubled Johnson graphs can be obtained as token graphs of the complete graph Kn and the star Sn = K1,n−1, respectively. Besides, we obtain a relationship between the spectra of the k-token graph of G and the k-token graph of its complement G. This generalizes to tokens graphs a wellknown property stating that the Laplacian eigenvalues of G are closely related to the Laplacian eigenvalues of G. Finally, the doubled odd graphs and doubled Johnson graphs provide two infinite families, together with some others, in which the algebraic connectivities of the original graph and its token graph coincide. Moreover, we conjecture that this is the case for any graph G and its token graph.This research of C. Dalfó and M.A. Fiol has been partially supported by AGAUR from the Catalan Government under project 017SGR1087 and by MICINN from the Spanish Government under project PGC2018-095471-B-I00. The research of C. Dalfó has also been supported by MICINN from the Spanish Government under project MTM2017-83271-R. The research of C. Huemer was supported by MICINN from the Spanish Government under project PID2019-104129GB-I00/AEI/10.13039/501100011033 and AGAUR from the Catalan Government under project 017SGR1336. F.J. Zaragoza Martínez acknowledges the support of the National Council of Science and Technology (Conacyt) and its National System of Researchers (SNI). This research has also received funding from the European Union’s Horizon 2020 research and innovation programme under the Marie Skłodowska-Curie grant agreement No 734922Elsevier202120212021info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttps://doi.org/10.1016/j.laa.2021.05.005http://hdl.handle.net/10459.1/71777http://hdl.handle.net/10459.1/71777reponame: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/PGC2018-095471-B-I00info: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/PID2019-104129GB-I00Reproducció del document publicat a https://doi.org/10.1016/j.laa.2021.05.005Linear Algebra and its Applications, 2021, vol. 625, p. 322-348info:eu-repo/grantAgreement/EC/H2020/734922cc-by-nc-nd (c) Dalfó et al., 2021info:eu-repo/semantics/openAccesshttp://creativecommons.org/licenses/by-nc-nd/4.0/oai:recercat.cat:10459.1/717772026-05-29T05:05:01Z |
| dc.title.none.fl_str_mv |
On the Laplacian spectra of token graphs |
| title |
On the Laplacian spectra of token graphs |
| spellingShingle |
On the Laplacian spectra of token graphs Dalfó, Cristina Token graph Laplacian spectrum Algebraic connectivity Binomial matrix Adjacency spectrum |
| title_short |
On the Laplacian spectra of token graphs |
| title_full |
On the Laplacian spectra of token graphs |
| title_fullStr |
On the Laplacian spectra of token graphs |
| title_full_unstemmed |
On the Laplacian spectra of token graphs |
| title_sort |
On the Laplacian spectra of token graphs |
| dc.creator.none.fl_str_mv |
Dalfó, Cristina Duque, F. Fabila Monroy, R. Fiol Mora, Miguel Ángel Huemer, Clemens Zaragoza Martínez, F.J. Trujillo Negrete, A.L. |
| author |
Dalfó, Cristina |
| author_facet |
Dalfó, Cristina Duque, F. Fabila Monroy, R. Fiol Mora, Miguel Ángel Huemer, Clemens Zaragoza Martínez, F.J. Trujillo Negrete, A.L. |
| author_role |
author |
| author2 |
Duque, F. Fabila Monroy, R. Fiol Mora, Miguel Ángel Huemer, Clemens Zaragoza Martínez, F.J. Trujillo Negrete, A.L. |
| author2_role |
author author author author author author |
| dc.subject.none.fl_str_mv |
Token graph Laplacian spectrum Algebraic connectivity Binomial matrix Adjacency spectrum |
| topic |
Token graph Laplacian spectrum Algebraic connectivity Binomial matrix Adjacency spectrum |
| description |
We study the Laplacian spectrum of token graphs, also called symmetric powers of 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. In this paper, we give a relationship between the Laplacian spectra of any two token graphs of a given graph. In particular, we show that, for any integers h and k such that 1 ≤ h ≤ k ≤ n 2 , the Laplacian spectrum of Fh(G) is contained in the Laplacian spectrum of Fk(G). We also show that the doubled odd graphs and doubled Johnson graphs can be obtained as token graphs of the complete graph Kn and the star Sn = K1,n−1, respectively. Besides, we obtain a relationship between the spectra of the k-token graph of G and the k-token graph of its complement G. This generalizes to tokens graphs a wellknown property stating that the Laplacian eigenvalues of G are closely related to the Laplacian eigenvalues of G. Finally, the doubled odd graphs and doubled Johnson graphs provide two infinite families, together with some others, in which the algebraic connectivities of the original graph and its token graph coincide. Moreover, we conjecture that this is the case for any graph G and its token graph. |
| publishDate |
2021 |
| dc.date.none.fl_str_mv |
2021 2021 2021 |
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info:eu-repo/semantics/article info:eu-repo/semantics/publishedVersion |
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article |
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publishedVersion |
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https://doi.org/10.1016/j.laa.2021.05.005 http://hdl.handle.net/10459.1/71777 http://hdl.handle.net/10459.1/71777 |
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https://doi.org/10.1016/j.laa.2021.05.005 http://hdl.handle.net/10459.1/71777 |
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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/PGC2018-095471-B-I00 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/PID2019-104129GB-I00 Reproducció del document publicat a https://doi.org/10.1016/j.laa.2021.05.005 Linear Algebra and its Applications, 2021, vol. 625, p. 322-348 info:eu-repo/grantAgreement/EC/H2020/734922 |
| dc.rights.none.fl_str_mv |
cc-by-nc-nd (c) Dalfó et al., 2021 info:eu-repo/semantics/openAccess http://creativecommons.org/licenses/by-nc-nd/4.0/ |
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cc-by-nc-nd (c) Dalfó et al., 2021 http://creativecommons.org/licenses/by-nc-nd/4.0/ |
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openAccess |
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Elsevier |
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Elsevier |
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