On Adjacent Vertex Distinguishing Total Coloring of the Joint Graph Wm∨Pn

A total-coloring is called adjacent vertex-distinguishing if the colored sets of evdy two adjacent vertices are different from each other.The minimum number of colors required for an adjacent vertex-distinguishing total coloring of a simple graph G is called the adjacent vertex-distinguishing total chromatic number,denoted by xat(G).In this paper,it has been given the adjacent vertex-distinguishing total chromatic number of Wm∨Pn with n≥4.