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On the metric dimension of two families of convex polytopes. (English) Zbl 1337.05032

Summary: A distance between two vertices of a connected graph is the shortest distance between them. The metric dimension of a connected graph \(G\) is the minimum cardinality of a subset \(W\) of vertices of \(G\) such that all vertices are uniquely determined by their distances from \(W\). A family \(\mathcal {G}\) of connected graphs is a family with constant metric dimension if \(\dim(G)\) is finite and does not depend upon the choice of \(G\) in \(\mathcal {G}\). In this paper we study the metric dimension of two classes of convex polytopes and show that these classes of convex polytopes have constant metric dimension.

MSC:

05C12 Distance in graphs
05C40 Connectivity
05C10 Planar graphs; geometric and topological aspects of graph theory
52A99 General convexity
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