线性六边形链图的半全控制数  

The semitotal domination number of the linear hexagonal chain

作　　者：宋曦 陈琴 SONG Xi;CHEN Qin(College of Sciences,China Jiliang University,Hangzhou 310018,China)

机构地区：[1]中国计量大学理学院,浙江杭州310018

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)。

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.

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 

分 类 号：O157.5[理学—数学]