On token signed graphs

We introduce the concept of a k-token signed graph and study some of its combinatorial and algebraic properties. We prove that two switching isomorphic signed graphs have switching isomorphic token graphs. Moreover, we show that the Laplacian spectrum of a balanced signed graph is contained in the L...

Descripción completa

Detalles Bibliográficos
Autores: Dalfó Simó, Cristina|||0000-0002-8438-9353, Fiol Mora, Miquel Àngel|||0000-0003-1337-4952, Steffen, Eckhard
Tipo de recurso: artículo
Fecha de publicación:2025
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:2117/450161
Acceso en línea:https://hdl.handle.net/2117/450161
https://dx.doi.org/10.1007/s10801-025-01416-4
Access Level:acceso abierto
Palabra clave:Token graph
Signed graph
Laplacian spectrum
Àrees temàtiques de la UPC::Matemàtiques i estadística::Matemàtica discreta
Àrees temàtiques de la UPC::Matemàtiques i estadística::Matemàtica discreta::Teoria de grafs
Descripción
Sumario:We introduce the concept of a k-token signed graph and study some of its combinatorial and algebraic properties. We prove that two switching isomorphic signed graphs have switching isomorphic token graphs. Moreover, we show that the Laplacian spectrum of a balanced signed graph is contained in the Laplacian spectra of its k-token signed graph. Besides, we introduce and study the unbalance level of a signed graph, which is a new parameter that measures how far a signed graph is from being balanced. Moreover, we study the relation between the frustration index and the unbalance level of signed graphs and their token signed graphs.