路、扇及星的Mycielski图的邻点可区别I-全染色  

Adjacent Vertex-Distinguishing I-Total Coloring of Some Mycielski Graphs of Path,Fan and Star

作　　者：刘秀丽[1] 

机构地区：[1]菏泽学院数学系,山东菏泽274015

出　　处：《中北大学学报（自然科学版）》2015年第4期408-411,共4页Journal of North University of China(Natural Science Edition)

基　　金：山东省自然科学基金资助项目(ZR2011AL018);山东省高校科技计划资助项目(J13LI02)

摘　　要：研究了Pn,Fn和Sn图的Mycielski图的邻点可区别的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).根据图M(Pn),M(Fn)和M(Sn)的构造特征,利用构造函数法,构造了一个从点边集V(G)∪E(G)到色集合{1,2,…,k}的函数,给出了一种染色方案,得到了M(Pn),M(Fn)和M(Sn)图的邻点可区别的I-全色数,并且满足猜想.Adjacent vertex-distinguishing I-total coloring of Mycielski graphs of graphs Pn,Fn and Sn were studied.Adjacent vertex-distinguishing I-total coloring of graph G was an map 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 byχiat（G）.By constructing the function from the vertices and edges set V（G）∪E（G）to the color set{1,2,…,k},a new coloring method is given according to the feature of graphs M（Pn）,M（Fn）and M（Sn）,and the adjacent vertex-distinguishing I-total chromatic number of them are obtained,which meet the suspect.

关 键 词：全染色 邻点可区别全染色 邻点可区别I-全染色 邻点可区别I-全色数 MYCIELSKI图 

分 类 号：O157.5[理学—数学]