Vertex strongly distinguishing total coloring of complete bipartite graph K3,3

Let f be a proper total coloring of G. For each x ∈ V(G), let C(x) denote the set of all colors of the elements incident with or adjacent to x and the color of x. If ∀u, v ∈ V(G), u ≠ v, we have C(u) ≠ C(v), then f is called a vertex strongly distinguishing total coloring of G. The minimum number k for which there exists a vertex strongly distinguishing total coloring of G using k colors is called the vertex strongly distinguishing total chromatic number of G. The vertex strongly distinguishing total chromatic number of complete bipartite graph K3,3is obtained in this paper.