On two algebras of token graphs

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dc.contributor.authorReyes, M. A.
dc.contributor.authorDalfó, Cristina
dc.contributor.authorFiol Mora, Miguel Ángel
dc.date.accessioned2026-10-02T07:32:28Z
dc.date.available2026-10-02T07:32:28Z
dc.date.issued2026
dc.description.abstractThe 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 are adjacent whenever their symmetric difference is a pair of adjacent vertices in G. In this article, we describe some properties of the Laplacian matrix Lk of Fk(G) and the Laplacian matrix L & strns;k of the k-token graph Fk(G & strns;) of its complement G & strns; . First, we provide a complete proof of a result from a previous article on the commutativity of the matrices Lk and L & strns;k . Based on this result, fixed the pair (n, k) and the graph G, we introduce a 'local' algebra L(G) , generated by the pair (Lk,L & strns;k) , showing its close relationship with the Bose-Mesner algebra of the Johnson graphs J(n, k). Finally, for fixed (n, k), we present a 'global' algebra A(n,k) that contains L(G) together with the Laplacian and adjacency matrices of the k-token graph of any graph G on n vertices.
dc.description.sponsorshipThis research has been supported by AGAUR from the Catalan Government under project 2021SGR00434 and MICINN from the Spanish Government under project PID2020-115442RB-I00. Also, it has a grant from the Research Vice-Rector of UdL.
dc.identifier10.1007/s40590-026-00937-7
dc.identifier.doihttps://doi.org/10.1007/s40590-026-00937-7
dc.identifier.issn1405-213X
dc.identifier.urihttps://hdl.handle.net/10459.1/471268
dc.language.isoeng
dc.publisherSpringer
dc.relationinfo:eu-repo/grantAgreement/ES/MICINN/PID2020-115442RB-I00
dc.relation.isformatofReproducció del document publicat a https://doi.org/10.1007/s40590-026-00937-7
dc.relation.ispartofBoletín de la Sociedad Matemática Mexicana, 2026, vol.32, núm.106
dc.rightscc-by, (c) Reyes, et al., 2026
dc.rightsAttribution 4.0 International*
dc.rights.accessRightsinfo:eu-repo/semantics/openAccess
dc.rights.urihttp://creativecommons.org/licenses/by/4.0/*
dc.subjectToken graph
dc.subjectBose-Mesner algebra
dc.subjectDistance-regular graphs
dc.subjectScience & Technology
dc.subjectPhysical Sciences
dc.titleOn two algebras of token graphs
dc.typeinfo:eu-repo/semantics/article
dc.type.versioninfo:eu-repo/semantics/publishedVersion
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