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arXiv · 1205.1334

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

Delia Garijo·Antonio González·Alberto Márquez
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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 $a\geq 4$ is realizable as the resolving number of an infinite family of graphs.

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Delia Garijo, Antonio González, Alberto Márquez. 2012-05-08. On the metric dimension, the upper dimension and the resolving number of graphs. https://arxiv.org/abs/1205.1334

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