On the fault-tolerant metric dimension of convex polytopes

Hassan Raza, Sakander Hayat and Xiang-Feng Pan

Applied Mathematics and Computation, 2018, vol. 339, issue C, 172-185

Abstract: A convex polytopes is a polytope that is also a convex set of points in the n-dimensional Euclidean space Rn. By preserving the same adjacency relation between vertices of a convex polytope, its graph is constructed. The metric dimension problem has been extensively studied for convex polytopes and other families of graphs. In this paper, we study the fault-tolerant metric dimension problem for convex polytopes. By using a relation between resolving sets and fault-tolerant resolving sets of graphs, we prove that certain infinite families of convex polytopes are the families of graphs with constant fault-tolerant metric dimension. We conclude the paper with some open problems.

Keywords: Metric dimension; Fault-tolerant metric dimension; Convex polytopes (search for similar items in EconPapers)
Date: 2018
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Citations: View citations in EconPapers (5)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:339:y:2018:i:c:p:172-185

DOI: 10.1016/j.amc.2018.07.010

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