The dominant metric dimension of generalized Petersen graph

The dominant metric dimension is the development of the concepts of the resolving set and the dominating set of graphs. In this research, the dominant metric dimension concept is applied to a generalize Petersen graph. The purpose of this research is to determine the dominant metric dimension of a generalized Petersen graph. The dominant metric dimension is the minimum cardinality of the dominant resolving set. The dominant metric dimension of a generalized Petersen graph is denoted by Ddim(P(n, k)) for natural number n, k where n > 2k. The minimum cardinality of dominating set of the graph G is called a dominating number of G, denoted by γ(G). The results of this research are the dominant metric dimension of the generalized Petersen graph Ddim(P(n, i)) = γ(P(n, i)) for i = {1,2} and Ddim(P(n, 3)) = γ(P(n, 3))+1 for n ≡ 8,14,20 (mod 24) and Ddim(P(n, 3)) = γ(P(n, 3)) for other n.