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...

Descripción completa

Detalles Bibliográficos
Autores: Reyes Quiróz, Mónica Andrea, Dalfó Simó, Cristina|||0000-0002-8438-9353, Messegué Buisan, Arnau|||0000-0002-7425-7592, Fiol Mora, Miquel Àngel|||0000-0003-1337-4952
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
Descripción
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.