View in EDS

Some results on the laplacian spectra of Token graphs

Saved in:
Bibliographic Details
Title: Some results on the laplacian spectra of Token graphs
Authors: Dalfó Simó, Cristina, Duque, Frank, Fabila Monroy, Ruy, Fiol Mora, Miquel Àngel, Huemer, Clemens, Trujillo Negrete, Ana Laura, Zaragoza Martínez, Francisco
Contributors: Universitat Politècnica de Catalunya. Departament de Matemàtiques, Universitat Politècnica de Catalunya. COMBGRAPH - Combinatòria, Teoria de Grafs i Aplicacions, Universitat Politècnica de Catalunya. DCG - Discrete and Combinatorial Geometry
Publisher Information: Springer
Publication Year: 2021
Collection: Universitat Politècnica de Catalunya, BarcelonaTech: UPCommons - Global access to UPC knowledge
Subject Terms: Àrees temàtiques de la UPC::Matemàtiques i estadística::Matemàtica discreta::Combinatòria, Àrees temàtiques de la UPC::Matemàtiques i estadística::Matemàtica discreta::Teoria de grafs, Combinatorial analysis, Graph theory, Token graph, Laplacian spectrum, Algebraic connectivity, Binomial matrix, Adjacency spectrum, Doubled odd graph, Doubled Johnson graph, Complement graph, Combinacions (Matemàtica), Grafs, Teoria de, Classificació AMS::05 Combinatorics::05E Algebraic combinatorics, Classificació AMS::05 Combinatorics::05C Graph theory
Description: This version of the contribution has been accepted for publication, after peer review but is not the Version of Record and does not reflect post-acceptance improvements, or any corrections. The Version of Record is available online at: http://dx.doi.org/10.1007/978-3-030-83823-2_11. Use of this Accepted Version is subject to the publisher's Accepted Manuscript terms of use http://www.spingernature.com/gp/open-research/policies/accepted-manuscript-terms. ; 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 work, 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=n2 , the Laplacian spectrum of Fh(G) is contained in the Laplacian spectrum of Fk(G) . 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 a well-known property for Laplacian eigenvalues of graphs to token graphs. ; The research of C. Dalf´o and M. A. Fiol has been 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 C. Dalf´o has also been supported by MICINN from the Spanish Government under project MTM2017-83271-R. The research of C. Huemer was supported by PID2019-104129GBI00/ AEI/ 10.13039/501100011033 and Gen. Cat. DGR 2017SGR1336. F. J. Zaragoza Mart´ınez acknowledges the support of the National Council of Science and Technology (Conacyt) and its National System of Researchers (SNI). This work has received funding from the European Union’s Horizon 2020 research and innovation programme under the Marie Sklodowska-Curie grant agreement No 734922. ; Peer Reviewed ; Postprint ...
Document Type: conference object
File Description: 7 p.; application/pdf
Language: English
Relation: https://link.springer.com/chapter/10.1007/978-3-030-83823-2_11; info:eu-repo/grantAgreement/EC/H2020/734922/EU/Combinatorics of Networks and Computation/CONNECT; info:eu-repo/grantAgreement/AEI/Plan Estatal de Investigación Científica y Técnica y de Innovación 2017-2020/PID2019-104129GB-I00/ES/TEORIA Y APLICACIONES DE CONFIGURACIONES DE PUNTOS Y REDES/; http://hdl.handle.net/2117/363817
DOI: 10.1007/978-3-030-83823-2_11
Availability: http://hdl.handle.net/2117/363817
https://doi.org/10.1007/978-3-030-83823-2_11
Rights: Open Access
Accession Number: edsbas.C04F5E5A
Database: BASE
Description
Abstract:This version of the contribution has been accepted for publication, after peer review but is not the Version of Record and does not reflect post-acceptance improvements, or any corrections. The Version of Record is available online at: http://dx.doi.org/10.1007/978-3-030-83823-2_11. Use of this Accepted Version is subject to the publisher's Accepted Manuscript terms of use http://www.spingernature.com/gp/open-research/policies/accepted-manuscript-terms. ; 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 work, 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=n2 , the Laplacian spectrum of Fh(G) is contained in the Laplacian spectrum of Fk(G) . 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 a well-known property for Laplacian eigenvalues of graphs to token graphs. ; The research of C. Dalf´o and M. A. Fiol has been 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 C. Dalf´o has also been supported by MICINN from the Spanish Government under project MTM2017-83271-R. The research of C. Huemer was supported by PID2019-104129GBI00/ AEI/ 10.13039/501100011033 and Gen. Cat. DGR 2017SGR1336. F. J. Zaragoza Mart´ınez acknowledges the support of the National Council of Science and Technology (Conacyt) and its National System of Researchers (SNI). This work has received funding from the European Union’s Horizon 2020 research and innovation programme under the Marie Sklodowska-Curie grant agreement No 734922. ; Peer Reviewed ; Postprint ...
DOI:10.1007/978-3-030-83823-2_11