On the metric dimension, the upper dimension and the resolving number of graphs

This paper deals with three resolving parameters: the metric dimension, the upper dimension and the resolving number. We first answer a question raised by Chartrand and Zhang asking for a characterization of the graphs with equal metric dimension and resolving number. We also solve in the affirmativ...

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Detalles Bibliográficos
Autores: Garijo Royo, Delia, González Herrera, Antonio, Márquez Pérez, Alberto
Tipo de recurso: artículo
Estado:Versión publicada
Fecha de publicación:2013
País:España
Institución:Universidad de Sevilla (US)
Repositorio:idUS. Depósito de Investigación de la Universidad de Sevilla
OAI Identifier:oai:idus.us.es:11441/38830
Acceso en línea:http://hdl.handle.net/11441/38830
https://doi.org/10.1016/j.dam.2013.01.026
Access Level:acceso abierto
Palabra clave:Resolving set
Metric dimension
Upper dimension
Resolving number
Descripción
Sumario:This paper deals with three resolving parameters: the metric dimension, the upper dimension and the resolving number. We first answer a question raised by Chartrand and Zhang asking for a characterization of the graphs with equal metric dimension and resolving number. We also solve in the affirmative a conjecture posed by Chartrand, Poisson and Zhang about the realization of the metric dimension and the upper dimension. Finally, we prove that no integer a≥4a≥4 is realizable as the resolving number of an infinite family of graphs.