Neighbor sum distinguishing edge colorings of graphs with bounded maximum average degree

dA proper lkl-edge coloring of a graph G is a proper edge coloring of G using colors of the set [k], where [k] = {1, 2,..., k}. A neighbor sum distinguishing vertical bar k vertical bar-edge coloring of G is a proper [k]-edge coloring of G such that, for each edge uv is an element of E(G), the sum of colors taken on the edges incident with u is different from the sum of colors taken on the edges incident with u. By ndi Sigma(G), we denote the smallest value k in such a coloring of G. The average degree of a graph G is Sigma vEV(G)d(v)/vertical bar V(G)vertical bar; we denote it by ad(G). The maximum average degree mad(G) of G is the maximum of average degrees of its subgraphs. In this paper, we show that, if G is a graph without isolated edges and mad(G) < 5/2, then ndi Sigma(G) <= k, where k = max {Delta(G) + 1, 6}. This partially confirms the conjecture proposed by Flandrin et al. (C) 2013 Elsevier B.V. All rights reserved.