Several Results On Vertex-distinguishing E-total Colorings Of Complete Bipartite Graph K_10,n

Let G be a simple graph.A total coloring f of G is called an E-total col-oring 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,if C?u??C?v?for any two distinct vertices u and v of V?G?,where C?x?denotes the set of colors of vertex x and of the edges incident with x under f,then f is called a vertex-distinguishing E-total coloring of G.Let Xvte?G?=min{k|G has a k-VDET coloring}.Then Xvte?G?is called the VDET chromatic number of G.By using analytical method and proof by contradiction,constructing the colorings,the VDET coloring of complete bipartite graph K_10,n is discussed and the VDET chromatic number of K_10,n has been obtained.