On the fault-tolerant metric dimension of convex polytopes

摘要

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.