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

Authors:
Delia Garijo;Antonio GonzáLez;Alberto MáRquez
Affiliations:
-;-;-
Venue:
Discrete Applied Mathematics
Year:
2013

Citing 3
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Landmarks in graphs

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On the Metric Dimension of Cartesian Products of Graphs

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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=4 is realizable as the resolving number of an infinite family of graphs.