Let G=(V, E) be an (n,m) graph. G is said to be strongly indexable if there exists a bijection ƒ: V→ {0, 1, 2, … …, n-1}, such that ƒ+ (E)={1,2, …, m}, where ƒ+ (u,v)=ƒ (u) + ƒ (v) for any Edge uv ε E. G is said to be indexable if ƒ+ is injective on E. In this paper we construct classes of indexable graphs, and we give an upper bound for the number of edges of any graph on vertices to be indexable. Also, we determine all indexable graphs of order ≤ 6.