Abstract: Firstly, we discussed vertex-distinguishing general total chromatic number of complete tripartite graphs K_3,5,p(p≥5) by using the method of distributing the color sets in advance and contradiction, and gave special proofs when p was small and regular proofs when p increased gradually. Secondly, we used the methods of constructing the colorings to dye the complete tripartite graphs K_3,5,p, and gave a  coloring scheme. The success of the coloring verified the correctness of the color number proved by the contradiction method, thus we solved the problem of vertex-distinguishing general total coloring of complete tripartite graphs K_3,5,p.

Key words: complete tripartite graph, general total coloring, vertex-distinguishing , general total coloring, vertexdistinguishing general total chromatic number