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Some results on the laplacian spectra of Token graphs

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some results on the Laplacian spectrum of token graphs_EuroComb2021.pdf (233,5Kb)
 
10.1007/978-3-030-83823-2_11
 
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hdl:2117/363817

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Dalfó Simó, CristinaMés informacióMés informació
Duque, Frank
Fabila Monroy, Ruy
Fiol Mora, Miquel ÀngelMés informacióMés informacióMés informació
Huemer, ClemensMés informacióMés informacióMés informació
Trujillo Negrete, Ana Laura
Zaragoza Martínez, Francisco
Document typeConference report
Defense date2021
PublisherSpringer
Rights accessOpen Access
All rights reserved. This work is protected by the corresponding intellectual and industrial property rights. Without prejudice to any existing legal exemptions, reproduction, distribution, public communication or transformation of this work are prohibited without permission of the copyright holder
ProjectCONNECT - Combinatorics of Networks and Computation (EC-H2020-734922)
TEORIA Y APLICACIONES DE CONFIGURACIONES DE PUNTOS Y REDES (AEI-PID2019-104129GB-I00)
Abstract
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.
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.
CitationDalfo, C. [et al.]. Some results on the laplacian spectra of Token graphs. A: European Conference on Combinatorics, Graph Theory and Applications. "Extended Abstracts EuroComb 2021: European Conference on Combinatorics, Graph Theory and Applications". Berlín: Springer, 2021, p. 64-70. ISBN 978-3-030-83822-5. DOI 10.1007/978-3-030-83823-2_11. 
URIhttp://hdl.handle.net/2117/363817
DOI10.1007/978-3-030-83823-2_11
ISBN978-3-030-83822-5
Publisher versionhttps://link.springer.com/chapter/10.1007/978-3-030-83823-2_11
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  • DCG - Discrete and Combinatorial Geometry - Ponències/Comunicacions de congressos [8]
  • COMBGRAPH - Combinatòria, Teoria de Grafs i Aplicacions - Ponències/Comunicacions de congressos [68]
  • Departament de Matemàtiques - Ponències/Comunicacions de congressos [1.137]
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