Neighbor Sum Distinguishing Colorings of Graphs with Maximum Average Degree Less Than 37/12

Let G be a graph and let its maximum degree and maximum average degree be denoted byΔ(G) and mad(G), respectively. A neighbor sum distinguishing k-edge colorings of graph G is a proper k-edge coloring of graph G such that, for any edge uv ∈ E(G), the sum of colors assigned on incident edges of u is different from the sum of colors assigned on incident edges of v. The smallest value of k in such a coloring of G is denoted by χ’∑≠(G). Flandrin et al. proposed the following conjecture thatχ’∑(G) ≤Δ(G) + 2 for any connected graph with at least 3 vertices and G≠C. In this paper, we prove that the conjecture holds for a normal graph with mad(G) <37/12 and Δ(G) ≥ 7.