Neighbor sum distinguishing total colorings of planar graphs with maximum degree Δ

A (proper) total [k]-coloring of a graph G is a mapping phi : V(G) boolean OR E(G) -> [k] = {1, 2,..., k} such that any two adjacent elements in V(G) boolean OR E(G) receive different colors. Letf (v) denote the sum of the color of a vertex v and the colors of all incident edges of v. A total [k]-neighbor sum distinguishing-coloring of G is a total [k]-coloring of G such that for each edge uv is an element of E(G), f(u) not equal f(v). BY chi(nsd)''(()G), we denote the smallest value k in such a coloring of G. In this paper, we show that if G is a planar graph with Delta(G) >= 14, then chi(nsd)''(G) <= Delta(G) + 2. (C) 2015 Elsevier B.V. All rights reserved.