Neighbor sum distinguishing index of 2-degenerate graphs

We consider proper edge colorings of a graph G using colors in $$\{1,\ldots ,k\}$$ { 1 , … , 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 $${\mathrm ndi}_{\Sigma }(G)$$ n d i Σ ( G ) . In this paper we show that if G is a 2-degenerate graph without isolated edges, then $${\mathrm ndi}_{\Sigma }(G)\le \max \{\Delta (G)+2,7\}$$ n d i Σ ( G ) ≤ max { Δ ( G ) + 2 , 7 } .