Vertex Distinguishing Ie-total Coloring And General-total Coloring Of K_3,n,p

The coloring theory of graphs arises from the practical problem of describing the relationship between points and points,and it has applications in many fields such as natural sciences or social sciences.Therefore,the research on the coloring theory of graphs has broad application prospects and important research value.Based on the research of vertex distinguishing normal-total coloring,this paper uses some new ideas such as“the method of distributing the color sets in advance”and“constructing the colorings”to explore vertex distinguishing general-total coloring and vertex distinguishing IE-total coloring of complete tripartite graph K_3,n,p,use the method of contradiction to prove the general law in segments and some special proofs that appear when the number of vertices in the graph is small,determine the vertex distinguishing IE-total chromatic number of K_3,n,p.And according to the similarity law of vertex distinguishing general-total chromatic number and vertex distinguishing IE-total chromatic number,a conjecture about vertex distinguishing general-total coloring of K_3,n,pis proposed.