Optimal Fault-Tolerant Resolving Set of Power Paths

In a simple connected undirected graph G, an ordered set R of vertices is called a resolving set if for every pair of distinct vertices u and v, there is a vertex (Formula presented.) such that (Formula presented.). A resolving set F for the graph G is a fault-tolerant resolving set if for each (Formula presented.), (Formula presented.) is also a resolving set for G. In this article, we determine an optimal fault-resolving set of r-th power of any path (Formula presented.) when (Formula presented.). For the other values of n, we give bounds for the size of an optimal fault-resolving set. We have also presented an algorithm to construct a fault-tolerant resolving set of (Formula presented.) from a fault-tolerant resolving set of (Formula presented.) where (Formula presented.).