Abstract:

A proper total coloring of the graph G is called vertex-distinguishing total coloring, if any two vertices have different color sets, where the color set of a vertex is the set composed of all colors of the vertex and the edges incident to it. On the base of the bound of vertex-distinguishing total chromatic number（ χ_vt ( G)≤|V(G)|+2）. The new upper bound of vertex-distinguishing total chromatic number is obtained by way of probability.

Key words:   vertex-distinguishing total coloring; vertex distinguishing total chromatic number;  the Lovász local lemma