Abstract: Taking the complete tripartite graphs K_1,1,p,K_1,2,p as examples, we discussed vertexdistinguishing IEtotal coloring and vertexdistinguishing general total coloring problem of the complete tripartite graphs  K_1,1,p,K_1,2,p by using the methods of the color sets prior distribution, constru
cting the dyeing and proofing by contradiction. We determined the vertexdistinguishing IEtotal coloring chromatic number and vertexdistinguishing general total chromatic number of K_1,1,p,K_1,2,p.

Key words: complete tripartite graph, vertexdistinguishing general total chromatic number, vertexdistinguishing IEtotal chromatic number