若干路的冠图的邻点可区别Ⅰ-全染色

Adjacent Vertex-Distinguishing Ⅰ-Total Coloring of Some Crown Graphs of Path

研究了若干路的冠图P_n°P_m,P_n°Cm,P_n°Fm和P_n°W_m的邻点可区别的Ⅰ-全染色.图G的邻点可区别的Ⅰ-全染色是从G的点边集V(G)∪E(G)到色集{1,2,…,k}的一个映射f,满足:任意uv∈E(G),u≠v,有f(u)≠f(v);任意uv,uw∈E(G),v≠w,有f(uv)≠f(uw);任意uv∈E(G),u≠v,有C(u)≠C(v),其中C(u)={f(u)}∪{f(uv)|uv∈E(G).最小的k值称为图G的邻点可区别的Ⅰ-全色数,记作χiat(G).根据路的冠图P_n°P_m,P_n°C_m,P_n°Fm和P_n°W_m的结构特征,利用构造映射法,构造了一个从集合V(G)∪E(G)到色集合{1,2,…,k}的映射,给出了一种染色方案,得到了它们的邻点可区别的Ⅰ-全色数.

Adjacent vertex-distinguishing Ⅰ-total coloring of some crown graphs of path Pn°Pm,Pn°Cm,Pn°Fm and Pn°Wm were studied.Adjacent vertex-distinguishing Ⅰ-total coloring of G was an assignment ffrom the vertices and edges set V（G）∪E（G）to the color set{1,2,…,k},such that：f（u）≠f（v）for any uv∈E（G）,u≠v;f（uv）≠f（uw）for any uv,uw∈E（G）,v≠ w;C（u）≠C（v）for any uv∈E（G）,u≠v,and C（u）={f（u）}∪{f（uv）｜uv∈E（G）.The minimum of k was called the adjacent vertex-distinguishing Ⅰ-total chromatic number and denoted by χ（at）~i（G）.By constructing the function fromV（G）∪E（G）to{1,2,…,k},a new coloring method was given according to the feature of these graphs,and the adjacent vertex-distinguishing Ⅰ-total chromatic numbers are obtained.