On the spectra of token graphs of cycles and other 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. It is a known result that the algebraic connectivity (or second Laplacian eigenvalue) of Fk(G) e...
| Autores: | , , , |
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| Tipo de recurso: | artículo |
| Estado: | Versión publicada |
| Fecha de publicación: | 2023 |
| País: | España |
| Institución: | Universitat de Lleida (UdL) |
| Repositorio: | Repositori Obert UdL |
| OAI Identifier: | oai:repositori.udl.cat:10459.1/464086 |
| Acceso en línea: | https://doi.org/10.1016/j.laa.2023.09.004 https://hdl.handle.net/10459.1/464086 |
| Access Level: | acceso abierto |
| Palabra clave: | Algebraic connectivity Binomial matrix Laplacian spectrum Lift graph Regular partition Token graph |
| Sumario: | 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. It is a known result that the algebraic connectivity (or second Laplacian eigenvalue) of Fk(G) equals the algebraic connectivity of G. In this paper, we first give results that relate the algebraic connectivities of a token graph and the same graph after removing a vertex. Then, we prove the result on the algebraic connectivity of 2-token graphs for two infinite families: the odd graphs Or for all r, and the multipartite complete graphs Kn for all n1,n2,…,nr In the case of cycles, we present a new method that allows us to compute the whole spectrum of F2(Cn). This method also allows us to obtain closed formulas that give asymptotically exact approximations for most of the eigenvalues of F2(Cn). |
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