Abstract: Let φ be a proper k-edge coloring of G. For each vertex v∈V(G), set f_φ(v)=∑_uv∈E(G)φ(uv). φ is called a k-neighbor sum distinguishing edge coloring of G if f_φ(u)≠f_φ(v) for each edge uv∈E(G). The smallest k such that G has a k-neighbor sum distinguishing edge coloring is called the neighbor sum distinguishing index, denoted by χ'_Σ(G). The neighbor sum distinguishing index of a kind of sparse graphs is determined. It is proved that if G is a graph without isolated edges, Δ≥6 and mad(G)≤5/2, then χ'_Σ(G)=Δ if and only if G has no adjacent vertices of maximum degree.

Key words: maximum average degree, neighbor sum distinguishing edge coloring, sparse graph