SOME NEW RESULTS ON THE ADJACENT VERTEX-DISTINGUISHING TOTAL COLORING OF GRAPHS

Under the definition of proper total coloring of a graph,an adjacent vertex-distinguishing total coloring means that none of the two adjacent vertices are incident with the same set of colores.The coloring set of vertex v was the colors assigned to v and the edges incident to v.The adjacent vertex-distinguishing total chromatic number of a graph G,denoted by χ_(at)(G),is the least number of colors required for an adjacent vertex-distinguishing total coloring of G.The adjacent vertex-distinguishing total chromatic number about some special graphs were provided.