On the adjacent-vertex-distinguishing total chromatic number of rK_2 V K_3

For a proper total coloring f of a simple G, the color set of a vertex v of G is the set of colors of edges incident with v together with the color assigned to v. For f, if any pair adjacent vertices have different color sets, then f is called an adjacent-vertex-distinguishing total coloring. The minimum number of colors in an adjacent-vertex-distinguishing total coloring is called the adjacent-vertex-distinguishing total chromatic number of G. The adjacent-vertex-distinguishing total chromatic number of rK_2∨K_s is discussed in this paper