Optimal Fault-Tolerant Resolving Set of Power Paths

In a simple connected undirected graph G, an ordered set R of vertices is called resolving if for every pair distinct u and v, there vertex w∈R such that d(u,w)≠d(v,w). A F the G fault-tolerant each v∈F, F∖{v} also G. this article, we determine optimal fault-resolving r-th power any path Pn when n≥r(r−1)+2. For other values n, give bounds size set. We have presented algorithm to construct Pmr from Pnr where m<n.