Vertex-Distinguishing IE-total Coloring And General-total Coloring Of K_1,n,p?1?n?6,n?p?

Graph coloring is one of the most important topics in graph theory research.Let G be a simple graph.A general total coloring f of G is defined as follows:V(G)UE(G)?[1,k].Once uv ? E(G),there is f(u)?f(v),then call f is IE-total coloring.For a k-IE—total coloring f of G[a general total coloring f of G]and any vertex x of G,let Cf(x)or C(x)denote the set of colors of vertex x and of the edges incident with x,that is C(x)={f(xu)|xu ? E} ?{f(x)}.We call C(x)the color set of x.If C(u)?C(v)for any two different vertices u and v of V(G),then f is called a vertex-distinguishing IE-total coloring(k-VDIETC)general vertex-distinguishing total coloring of G.Denote Xvtie(G)?min{k|G has k-VDIETC}.Which is called the vertex-distinguishing IE-total chromatic number of G,?gvt(G)=min{k| G has general vertex-distinguishing total coloringlis called the vertex-distinguishing general total chromatic number of G.the vertex-distinguishing general total coloring of G is also called general vertex-distinguishing total coloring.so we abbreviate it to GVDTC.For each graph G,we use ni=n.i(G)express the number of vertex which degree is i,?(G)? i??(G),?(G)meet demand(1l)+(2l)+(3l)+…+(s+1l)>?n?+n?+1?… +ns,??s??.The minium positive integer set up for every number.we will probe the question on vertex-distinguishing IE-total colorings and general vertex-distinguishing total colorings of K1,n,p(1?n?6,n ?p)by using the method of proof by contradiction?combinatorial analysis and constructing the concrete colorings.The vertex-distinguishing IE?total colorings and general vertex-distinguishing total colorings of K1,n,p(1?n?6,n?p)are determined in this paper.The conclusions of the paper shows that,for this graph,?vtie(K1,n,p)[?gzvt(K1,p,p)]=?(K1,n,p)+1 or?(K1,n,p).