(untitled) (Communications in Mathematical Research, 2021)
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 , 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 χ^e_vt(G) and is called the VDET chromatic number of G. The VDET coloring of complete bipartite graph K_7,n (7 ≤ n ≤ 95) is discussed in this paper and the VDET chromatic number of K_7,n (7 ≤ n ≤ 95) has been obtained.