Vertex Distinguishing IE-total Coloring And General-total Coloring Of K_2,n,p?2?n?5,n?p?

With the wide application of graph coloring in real life,it has gradually become one of the important fields studied by many scholars.A general total coloring of graph G refers to an assignment of all vertices and all edges of graph G with k colors of 1,2,…,k;A general total coloring f of graph G is called an IE-total coloring,if no two adjacent vertices of graph G receive the same color;For a total coloring f of graph G and any vertex x of G,record the set of the colors of x and the colors associated with x under f as Cf(x)or C(x)(non-multiple set),which is called the color set of vertex x under f;Let g is a general-total coloring[resp.IE-total coloring]if C(u)? C(v)for any two different vertices u and v in V(G),then g is called a vertex distinguishing general-total coloring[resp.vertex distinguishing IE-total coloring or VDIETC for short]of graph G.Vertex distinguishing general-total coloring can also be called general vertex distinguishing total coloring,so it simply be marked as GVDTC;The minimum number of color required for a GVDT coloring[resp.VDIET coloring]of graph G which is denoted by xgvt(G)[resp.xvtie(G)]is called GVDT chromatic number[resp.VDIET chromatic number]of graph G.In this paper,we will discuss the question on vertex distinguishing general-total coloring and vertex distinguishing IE-total coloring of complete tripartite graphs K2,n,p(2?n?5,n?p)by using the method of distributing the color sets in advance,constructing the colorings and contradiction.The vertex distinguishing general-total chromatic number and vertex distinguishing IE-total chromatic number of K2,n,p(2?n?5,n?p)are determined in this paper.