摘要
目的:研究线性六边形链图H m的半全控制数γt2(H m),其中H m表示由m个六边形组成的线性链图。方法:首先给出γt2(H m)和γt2(H m+3)的一个关系式,通过归纳法得到γt2(H m)的一个下界;再通过构造法给出线性六边形链图H m的一个半全控制集,得到γt2(H m)的一个上界;最后比较所得的上界和下界值,得到线性六边形链图的半全控制数。结果:确定了线性六边形链图H m的半全控制数并且给出一个基数最小的半全控制集。结论:对于由m个六边形组成的线性六边形链图H m,其半全控制数为γt2(H m)=(4m+1)/3+1。
Aims:This paper aims to study the semitotal domination numberγt2(H m)of the linear hexagonal chain H m,where H m denotes the linear hexagonal chain consisting of m hexagons.Methods:Firstly,a relationship betweenγt2(H m)andγt2(H m+3)was given.Then by the method of induction,a lower bound ofγt2(H m)was obtained.Next,an upper bound ofγt2(H m)was got by constructing a semitotal dominating set of the linear hexagonal chain H m.Finally,the upper bound and the lower bound ofγt2(H m)were compared to determine the semitotal domination number of the linear hexagonal chain H m.Results:The semitotal domination number of the linear hexagonal chain H m was got and a semitotal dominating set with minimum size was found.Conclusions:For the linear hexagonal chain H m consisting of m hexagons,the semitotal domination number isγt2(H m)=(4m+1)/3+1.
作者
宋曦
陈琴
SONG Xi;CHEN Qin(College of Sciences,China Jiliang University,Hangzhou 310018,China)
出处
《中国计量大学学报》
2020年第4期514-518,共5页
Journal of China University of Metrology
基金
国家自然科学基金项目(No.11701542)。
关键词
控制集
控制数
半全控制集
半全控制数
线性六边形链图
dominating set
domination number
semitotal dominating set
semitotal domination number
linear hexagonal chain
