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 some
shortest 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 two
distinct vertices of G are strongly resolved by some vertices of S. The strong metric dimension
of G, denoted by sdim(G), is de ned as the smallest cardinality of a strong resolving set. In
this paper, we determine the strong metric dimension of an antiprism An graph, a king Km;n
graph, and a Km ? Kn graph. We obtain the strong metric dimension of an antiprim graph
An are n for n odd and n + 1 for n even. The strong metric dimension of King graph Km;n is
m+n−1. The strong metric dimension of Km ?Kn graph are n for m = 1, n ≥ 1 and mn−1
for m ≥ 2, n ≥ 1.
