文章摘要
张婷,朱恩强,赵双柱,杜佳.若干Mycielski图邻点可区别Ⅰ-均匀全染色[J].,2018,58(5):547-550
若干Mycielski图邻点可区别Ⅰ-均匀全染色
Incidence-adjacent vertex distinguishing equitable total coloring of some Mycielski graphs
  
DOI:10.7511/dllgxb201805016
中文关键词: Mycielski图  邻点可区别Ⅰ-均匀全染色  邻点可区别Ⅰ-均匀全色数
英文关键词: Mycielski graph  incidence-adjacent vertex distinguishing equitable total coloring  incidence-adjacent vertex distinguishing equitable total chromatic number
基金项目:国家自然科学基金资助项目(60974112);中国博士后科学基金资助项目(2015M580928).
作者单位
张婷,朱恩强,赵双柱,杜佳  
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中文摘要:
      图G的一个邻点可区别Ⅰ-均匀全染色是指对图G的邻点可区别的一个Ⅰ-全染色f,若f还满足Ti-Tj≤1(i≠j),其中Ti=Vi∪Ei={vv∈V(G),f(v)=i}∪{ee∈E(G),f(e)=i},则称f为图G的一个邻点可区别Ⅰ-均匀全染色,而图G的邻点可区别Ⅰ-均匀全染色中所用的最少颜色数称为图G的邻点可区别Ⅰ-均匀全色数.通过函数构造法,得到了M(Pn)、M(Cn)、M(Sn)的邻点可区别Ⅰ-均匀全色数,并且满足猜想.
英文摘要:
      The incidence-adjacent vertex distinguishing equitable total coloring of graph Gis that to the incidence-adjacent vertex distinguishing total coloring fof graph G, if fsatisfies Ti-T j≤1 (i≠j), where Ti=Vi∪Ei={vv∈V(G), f(v)=i}∪{ee∈E(G), f(e)=i}, then fis called the incidence-adjacent vertex distinguishing equitable total coloring of graph G. The minimum number of colors required in incidence-adjacent vertex distinguishing equitable total coloring is called incidence-adjacent vertex distinguishing equitable total chromatic number of graph G. The incidence-adjacent vertex distinguishing equitable total chromatic numbers of M(Pn), M(Cn), M(Sn) are obtained by function construction methods, which meet the suspect.
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