Department of Mathematics, Faculty of Mathematics and Natural Sciences, Universitas Sebelas Maret, Surakarta, Indonesia E-mail: milawidyaningrum4@gmail.com, tri.atmojo.kusmayadi@gmail.com Abstract. Let G be a connected graph with vertex set V (G) and edge set E(G). The interval I[u, v] between u and v is defined as the collection of all vertices that belong to some shortest u-v path. A vertex s ∈ V (G) strongly resolves two vertices u and v if u belongs to a shortest v-s path or v belongs to a shortest u-s path. A set S ⊂ V (G) is a strong resolving set if every two distinct vertices of G are strongly resolved by some vertex of S. The smallest cardinality of strong resolving set is called a strong metric basis. The strong metric dimension of G, denoted by sdim(G), is defined as the cardinality of the strong metric basis. In this paper we determine the strong metric dimension of a sun graph Sn, a windmill graph Km n , and a M¨obius ladder graph Mn. We obtain the strong metric dimension of sun graph Sn is n - 1 for n ≥ 3. The strong metric dimension of windmill graph Km n is (n - 1)m - 1 for m ≥ 2 and n ≥ 3. The strong metric dimension of M¨obius ladder graph Mn with n ≥ 5 is 2⌈ n+2 4 ⌉ for n even.
