Adjacent Vertex Distinguishing Total Chromatic Number on S_m∨P_n

Let G be a simple connected graph.A-proper total coloring of is called adjacent distinguishing if for arbitrary two adjacent vertexand,,where is the set of the colors of and the edges are adjacent to.The minimum such that has a-adjacent-vertex-distinguishing total coloring is called the adjacent vertex distinguishing total chromatic number.The paper mainly presents the adjacent vertex distinguishing total chromatic number for the graph formed by a star and a path,and then a conjecture is raised.