Fault Tolerant Partition Resolvability in Convex Polytopes

摘要

Convex polytopes are special types of polytopes having an additional property that they are also convex sets in the n-dimensional Euclidean space. The convex polytope topologies are being used in the antitracking networks due to their stability, resilience, and destroy-resistance. The metric related parameters have been extensively studied in the recent times due to their applications in several areas including robot navigation, network designing, image processing, and chemistry. In this article, the sharp bounds for the fault tolerant partition dimension of certain well-known families of convex polytopes Rn, Qn, Sn, Tn, and Dn have been computed. Furthermore, we have studied the graphs having fault tolerant partition dimension bounded below by 4.