A graph G is said to be one modulo three mean graph if there is an injective function φ from the vertex set of G to the set {a|0 ≤ a ≤ 3q— 2 and either a ≡ 0(mod 3) or a ≡ 1(mod 3)} where q is the number of edges G and φ induces a bijection φ* from the edge set of G to {a|1 ≤ a ≤ 3q — 2 and either a ≡ 1(mod 3)} given byand the function φ is called one modulo three mean labeling of G. In this paper, we prove that the graphs T ° Kn, T ô K1,n, T ô Pn and T ô 2Pn are one modulo three mean graphs.