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...

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Detalhes bibliográficos
Autores: Dalfó, Cristina, Fiol Mora, Miguel Ángel, Steffen, E.
Formato: artículo
Estado:Versión publicada
Fecha de publicación:2025
País:España
Recursos:Universitat de Lleida (UdL)
Repositorio:Repositori Obert UdL
OAI Identifier:oai:repositori.udl.cat:10459.1/468422
Acesso em linha:https://doi.org/10.1007/s10801-025-01416-4
https://hdl.handle.net/10459.1/468422
Access Level:acceso abierto
Palavra-chave:Token graph
Signed graph
Laplacian spectrum
Descrição
Resumo: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.