Fault-Tolerant Metric Dimension of Cube of Paths

Abstract

For a simple connected graph G = (V (G), E(G)), a set R ⊆ V (G) is said to be a resolving set of G if every pair of vertices of G are resolved by some vertices in R i.e., every pair of vertices of G are identified uniquely by some vertex elements in F. A resolving set of G containing the minimum number of vertices is the metric basis and the minimum cardinality of the metric basis is called the metric dimension of G. A resolving set F for the graph G is said to be fault tolerant if for each u ∈ F, F \\ {u} is also a resolving set for G and the minimum cardinality of the fault-tolerant resolving set said to be the fault-tolerant metric dimension. In this article, we determine the exact value of fault-tolerant metric dimension of .