Abstract: With the help of existing conclusions of vertex distinguishing IEtotal colorings of complete bipartite graphs K_2,n and K_3,n, we discussed the question on general vertexdistinguishing total colorings of complete bipartite graphs K_2,n and K_3,n by using the method of combinatorial analysis and constructing the specific colorings, and determined the general vertexdistinguishing total chromatic numbers of K_2,nand K_3,n.

Key words: general total coloring, general vertexdistinguishing total chromatic number, complete bipartite graphs, general vertexdistinguishing total coloring