设G是简单图,图G的一个k-点可区别Ⅳ-全染色(简记为k-VDIVT染色)f是指一个从V(G)UE(G)到{1,2,…,k}的映射,满足:uv,uw∈E(G),v≠w,有f(uv)≠f(uw);u,v∈V(G),u≠v,有C(u)≠G(v),其中C(u)={f(u)}∪{f(uv)|uv∈E(G)}.数min{k|G有一个k-VDIVT染色}称为图的点可区别Ⅳ-全色数,记为χ_(vt)~(iv)(G).本文给出了双星S_(2n),轮W_n和扇F_n的点可区别Ⅳ-全色数.
Let G be a simple graph.An Ⅳ-total coloring f of G refers to a coloring of the vertices and edges of G so that no two adjacent edges receive the same color.Let C(u) be the set of colors of vertex u and edges incident to u under f.For an Ⅳ-total coloring f of G using k colors,if C(u)≠C(v) for any two different vertices u and v of V(G),then f is called a k-vertex-distinguishing Ⅳ-total-coloring of G,or a k-VDIVT coloring of G for short.The minimum number of colors required for a VDIVT coloring of G is denoted by x_(vt)~(iv)(G),and it is called the VDIVT chromatic number of G.We will give VDIVT chromatic numbers for double star S_(2n),wheel W_n and fan F_n in this article.