Fault-tolerant metric dimension of P(n, 2)ʘK₁ graph

Abstract

An ordered set W of vertices in a graph G is said to resolve G if every vertex in G is uniquely determined by its vector of distances to the vertices in W. A resolving set containing a minimum number of vertices is called a metric basis for G and the cardinality of such a set is its metric dimension denoted by dim(G). A resolving set W for G is fault-tolerant if W\{w} is also a resolving set, for each w ∈ W, and the fault-tolerant metric dimension of G is the minimum cardinality of such a set. In this paper we introduce the study of the fault-tolerant metric dimension of P(n, 2)ʘK₁ graph.

Subject Classification:

• 05C12

Keywords:

• Fault-tolerant
• Metric dimension
• Basis
• Resolving set
• Corona product
• Petersen graph