Vertex strongly distinguishing total coloring of complete bipartite graph K<inf>3,3</inf>

Abstract

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, 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 K3,3 is obtained in this paper. MR(2000) Subject classification: 05C15