Neighbor sum distinguishing index of 2-degenerate graphs

We consider proper edge colorings of a graph G using colors in ({1,ldots ,k}). Such a coloring is called neighbor sum distinguishing if for each pair of adjacent vertices u and v, the sum of the colors of the edges incident with u is different from the sum of the colors of the edges incident with v. The smallest value of k in such a coloring of G is denoted by ({mathrm ndi}_{Sigma }(G)). In this paper we show that if G is a 2-degenerate graph without isolated edges, then ({mathrm ndi}_{Sigma }(G)le max {Delta (G)+2,7}).