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 () 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 grap...

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Detalles Bibliográficos
Autores: Reyes, Mónica Andrea, Dalfó, Cristina, Fiol Mora, Miguel Ángel, Massagué Buisan, Arnau
Tipo de recurso: artículo
Estado:Versión publicada
Fecha de publicación:2025
País:España
Institución:Universitat de Lleida (UdL)
Repositorio:Repositori Obert UdL
OAI Identifier:oai:repositori.udl.cat:10459.1/466694
Acceso en línea:https://doi.org/10.1016/j.dam.2024.09.031
https://hdl.handle.net/10459.1/466694
Access Level:acceso abierto
Palabra clave:Token graph
Laplacian spectrum
Lift graph
Over-lift graph
Continous fraction
Descripción
Sumario:The k-token graph () 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 ()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.