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 |
| Sumario: | 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. |
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