科研之友
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摘要
A proper [k]-edge coloring of a graph G is a proper edge coloring of G using colors from [k] = {1, 2,..., k}. A neighbor sum distinguishing [k]-edge coloring of G is a proper [k]edge coloring of G such that for each edge uv epsilon E(G), the sum of colors taken on the edges incident to u is different from the sum of colors taken on the edges incident to v. By nsdi(G), we denote the smallest value k in such a coloring of G. It was conjectured by Flandrin et al. that if G is a connected graph without isolated edges and G not equal C-5, then nsdi(G) <= Delta(G) +2. In this paper, we show that if G is a planar graph without isolated edges, then nsdi(G) <= max{Delta(G) + 10, 25}, which improves the previous bound (max{2 Delta(G) + 1, 25}) due to Dong and Wang.
