  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
$a\geq 4$ is realizable as the resolving number of an infinite family of
graphs.
