Asymptotic Behavior of the Adjacent Vertex Distinguishing Total Coloring of Graphs

A proper k—total coloring is called adjacent vertex distinguishing total coloring if any two adjacent vertices have different color sets.The least number of colours required for a adjacent vertex distinguishing total coloring is called adjacent vertex distinguishing total chromatic number.Zhang conjectured that,for connected graph,the adjacent vertex distinguishing total chromatic number is at most △(G)+3.In this paper,using the probablistic methods,we prove that for any simple graph G,△≥ 14,then X_(at)(G) ≤ A + C,where C ≥ 10~(26) + 1.