On metric dimension of P(n, 2)ʘK₁ graph

Abstract

For a connected graph G, a subset W = {w₁, w₂, w₃, … , w_ξ} of the vertices of G is the resolving set for G if for a, b ∈ V(G), we have d(a, w_ξ) ≠ d(b, w_ξ) for all w_ξ ∈ W. Metric basis for G is the minimum number of vertices in W and metric dimension is the cardinality of such a set denoted by β (G). In this paper we compute the metric dimension of P(n, 2)ʘK₁.

Subject Classification:

• 05C12

Keywords:

• Metric dimension
• Basis
• Resolving set
• Corona product
• Petersen graph