On the metric dimension, the upper dimension and the resolving number of graphs
Combinatorics
2012-05-09 v2
Abstract
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 is realizable as the resolving number of an infinite family of graphs.
Cite
@article{arxiv.1205.1334,
title = {On the metric dimension, the upper dimension and the resolving number of graphs},
author = {Delia Garijo and Antonio González and Alberto Márquez},
journal= {arXiv preprint arXiv:1205.1334},
year = {2012}
}