The Adjacent Vertex Strongly Distinguishing Total Chromatic Number of the Graph

Graph coloring is one of the main contents of graph theory.It has wide applications in communication line design,algorithmic analysis,design and theory computer and so on.In recent years,more and more people start to study graph coloring.How to determine the chromatic number is the main issue in the coloring.The probabilistic method is a new way that studies graph coloring.It mainly estimates the upper bounds of the the chromatic number of graph coloring.The adjacent vertex strongly distinguishing total coloring of the graph is stuied by the probabilistic method and an upper bound of the adjacent vertex strongly distinguishing total coloring of the graph is gained.