Abstract. Let G be a connected graph with a set of vertices V (G) and a set of edges E(G).The interval I[u; v] between u and v to be the collection of all vertices that belong to someshortest u-v path. A vertex s ∈ V (G) is said to be strongly resolved for vertices u, v ∈ V (G)if v ∈ I[u; s] or u ∈ I[v; s]. A vertex set S ⊆ V (G) is a strong resolving set for G if every twodistinct vertices of G are strongly resolved by some vertices of S. The strong metric dimensionof G, denoted by sdim(G), is de ned as the smallest cardinality of a strong resolving set. Inthis paper, we determine the strong metric dimension of an antiprism An graph, a king Km;ngraph, and a Km ? Kn graph. We obtain the strong metric dimension of an antiprim graphAn are n for n odd and n + 1 for n even. The strong metric dimension of King graph Km;n ism+n−1. The strong metric dimension of Km ?Kn graph are n for m = 1, n ≥ 1 and mn−1for m ≥ 2, n ≥ 1.