Neighbor Sum Distinguishing Total Coloring Of Two Kinds Of Planar Graphs

Let ?:V(G)?E(G)?{1,2,...,k} be a proper k-total coloring of a graph G such that any two adjacent or incident elements of G have different colors.Let f(v)=?uv?E(G)?(uv)+?(v).The coloring 0 is a k-neighbor sum distinguishing total coloring of G if f(u)?f(v)for each edge uv?E(G),and the smallest value k is called the neighbor sum distinguishing total chromatic number,denoted by?"?(G).We mainly discuss that the neighbor sum distinguishing total colorings of pla-nar graphs with girth at least 5 and planar graphs without maximum degree vertices in this paper.By using Euler's formula,Combinatorial Nullstellensatz and discharging method,we get the following results.1.Let G be a planar graph with g(G)?>5,then ?"?(G)?max{?(G)+2,8}.2.Let G be a planar graph with g(G)?5 and ?(G)?7,If G has no adjacent?(G)-vertices,then ?"?(G)=?(G)+1,otherwise ?"?(G)=?(G)+2.3.Let G be a planar graph and ?(G)? 13,If G has no adjacent ?(G)-vertices,then ?"?(G)=?(G)+1,otherwise ?"?(G)=?(G)+2.