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This paper deals with three resolving parameters: the metric dimension, theupper dimension and the resolving number. We first answer a question raised byChartrand and Zhang asking for a characterization of the graphs with equalmetric dimension and resolving number. We also solve in the affirmative aconjecture posed by Chartrand, Poisson and Zhang about the realization of themetric dimension and the upper dimension. Finally we prove that no integer$a\geq 4$ is realizable as the resolving number of an infinite family ofgraphs.

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