Vertex-Distinguishing E-Total Coloring of Complete Bipartite Graph K7,n when n ≥ 978.

Let G be a simple graph. A total coloring f of G is called an E-total coloring if no two adjacent vertices of G receive the same color, and no edge of G receives the same color as one of its endpoints. For an E-total coloring f of a graph G and any vertex x of G, let C (x) denote the set of colors of vertex x and of the edges incident with x, we call C (x) the color set of x. If C (u) = C (v) for any two different vertices u and v of V (G), then we say that f is a vertex-distinguishing E-total coloring of G or a VDET coloring of G for short. The minimum number of colors required for a VDET coloring of G is denoted by xeVt (G) and is called the VDET chromatic number of G. The VDET coloring of complete bipartite graph K7,n (n ≥ 978) is discussed in this paper and the VDET chromatic number of K7,n (n ≥ 978) has been obtained. [ABSTRACT FROM AUTHOR]