A general method to find the spectrum and eigenspaces of the k-token graph of a cycle, and 2-token through continuous fractions
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 paper, we propose a general method to find the spectrum and eigenspaces of the k-token g...
| Autores: | , , , |
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| Tipo de recurso: | artículo |
| Fecha de publicación: | 2024 |
| País: | España |
| Institución: | Universitat Politècnica de Catalunya (UPC) |
| Repositorio: | UPCommons. Portal del coneixement obert de la UPC |
| Idioma: | inglés |
| OAI Identifier: | oai:upcommons.upc.edu:2117/419796 |
| Acceso en línea: | https://hdl.handle.net/2117/419796 https://dx.doi.org/10.1016/j.dam.2024.09.031 |
| Access Level: | acceso abierto |
| Palabra clave: | Token graph Laplacian spectrum Lift graph Over-lift graph Continuous fraction Àrees temàtiques de la UPC::Matemàtiques i estadística |
| 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. In this paper, we propose a general method to find the spectrum and eigenspaces of the k-token graph Fk(Cn) of a cycle Cn. The method is based on the theory of lift graphs and the recently introduced theory of over-lifts. In the case of k = 2, we use continuous fractions to derive the spectrum and eigenspaces of the 2-token graph of Cn. |
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