Abstract:

Let G be a simple graph, f is a total coloring of G. 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 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 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. Based on the analytical method and proof by contradiction, the VDET coloring of complete bipartite graph K_3,n was discussed and the VDET chromatic number of K_3,n(3≤n≤17) was obtained.

Key words: complete bipartite graphs, E-total coloring, vertexdistinguishing E-total coloring, vertexdistinguishing E-total chromatic number