Several Results On Vertex-distinguishing E-total Colorings Of Complete Bipartite Graph K_8,n

Let χvte(G)represent the smallest positive integer k satisfying the following condition:there exists an assignment of k colors to vertices and edges of G,such that the adjacent vertices in G receive different colors,and each edge and its end vertex receive different colors,and the set composed of the color of u and colors of edges incident with u is different from the set composed of the color of v and colors of edges incident with v.Such coloring is called a vertex-distinguishing E-total coloring of G,abbreviated as VDET coloring.The number χvte(G)is called VDET chromatic number of G.By using the method of combinatorial analysis,proof by contradiction,pre-allocation of color sets and constructing the colorings,the VDET coloring of complete bipartite graph K8,n is discussed and the VDET chromatic number of K8,n has been obtained.