Garijo Royo, DeliaGonzález Herrera, AntonioMárquez Pérez, Alberto2016-03-182016-03-182013Garijo Royo, D., González Herrera, A. y Márquez Pérez, A. (2013). On the metric dimension, the upper dimension and the resolving number of graphs. Discrete Applied Mathematics, 161 (10/11/17), 1440-1447. https://doi.org/http://dx.doi.org/10.1016/j.dam.2013.01.026.http://hdl.handle.net/11441/38830This 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.application/pdfengAttribution-NonCommercial-NoDerivatives 4.0 Internacionalhttp://creativecommons.org/licenses/by-nc-nd/4.0/Resolving setMetric dimensionUpper dimensionResolving numberinfo:eu-repo/semantics/articleinfo:eu-repo/semantics/openAccesshttps://doi.org/10.1016/j.dam.2013.01.026