k-Metric Dimension of Generalized Fan Graph and Cm ∗2 Kn Graph

Abstract

Let G be a simple connected graph with the vertex set V(G) and the set edge E(G). The set S ⊆ V(G) is called the kmetric generator on G if and only if every two different vertices in G are distinguished by at least k elements in S, in other words for every two different vertices u, v ∈ V(G), there are at least k vertices w 1 , w 2 , … , w k ∈ S such that d(u, w i ) ≠ d(v, w i ), for every i ∈ {1, … , k}. The k-metric generator with the smallest cardinality is called the k-metric base and the cardinality of the k-metric base is on call the k-metric dimension of the graph G denoted dim k (G). In this study, the k-metric dimension was obtained in generalized fan F m,n graph with m ≥ 1, n ≥ 3 and C m * 2 K n graph with m ≥ 3, n ≥ 2.