In this paper, we introduce a new labeling called one modulo three mean labeling. A graph G is said to be one modulo three mean graph if there is an injective function 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 of G and induces a bijection from the edge set of G to given by and the function is called one modulo three mean labeling of G. Furthermore, we prove that some standard graphs are one modulo three mean graphs.
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