Abstract: We considered vertexdistinguishing Etotal coloring of complete bipartite graph K_6,n(6≤n≤38), and gave the vertexdistinguishing Etotal coloring of a class of special complete bipartite graph by using the methods of combinatorial analysis, reduction to absurdity and constructing concrete colorings. The results show that the vertexdistinguishing Etotal chromatic number of complete bipartite graph K_6,n is 5 when 6≤n≤10 and is 6 when 11≤n≤38.

Key words: vertexdistinguishing Etotal chromatic number, Etotal coloring, vertexdistinguishing Etotal coloring, complete bipartite graph