Neighbor sum distinguishing edge colorings of sparse graphs

We consider proper edge colorings of a graph G using colors of the set {1,..., k}. Such a coloring is called neighbor sum distinguishing if for any uv is an element of E(G), the sum of colors of the edges incident to u is different from the sum of the colors of the edges incident to v. The smallest value of k in such a coloring of G is denoted by ndi(Sigma)(G). Let mad(G) and Delta(G) denote the maximum average degree and the maximum degree of a graph G, respectively. In this paper we show that, for a graph G without isolated edges, if mad(G) < 8/3, then ndi(Sigma)(G) <= max{Delta(G) + 1,7}; and if mad(G) < 3, then ndi(Sigma)(G) <= max {Delta(G) + 2,7}. (C) 2015 Elsevier B.V. All rights reserved.