| 关于图的反符号全控制 |
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| 引用本文： | 孔祥阳,徐保根.关于图的反符号全控制[J].宜春学院学报,2012,34(8):4-6. |
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| 作者姓名： | 孔祥阳 徐保根 |
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| 作者单位： | 1. 四川工程职业技术学院基础教学部,四川德阳,618000
2. 华东交通大学基础科学学院,南昌,330013 |
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| 摘 要： | 设G=（V,E）是一个图,一个函数f：V∪E→{-1,＋}1,如果对每一个x∈E∪V,都有∑y∈Ntx]f（y）≤0成立,则称f为图G的一个反符号全控制函数,其中Nt（x）表示G中与元素x相邻或相关联的元素之集,称为元素x的全邻域,Ntx]=N（x）∪{x}为x的闭全邻域。规定图G的反符号全控制数定义为γrst（G）=max{∑x∈V∪Ef（x）f为图的反符号全控制函数}。得到了一般图的反符号全控制数的若干上界,并确定了圈Cn的反符号全控制数。
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| 关 键 词： | 符号全控制函数符号 全控制数 反符号全控制函数 反符号全控制数 |
On Reverse Signed Total Domination in Graphs |
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| KONG Xiang-yang,XU Bao-gen.On Reverse Signed Total Domination in Graphs[J].Journal of Yichun University,2012,34(8):4-6. |
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| Authors: | KONG Xiang-yang XU Bao-gen |
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| Institution: | 1.Ministry of Basic Education,Sichuan Engineering Technical College,Deyang 618000,China; 2.School of Natural Science,East China Jiaotong University,Nanchang 330013,China) |
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| Abstract: | Let G=(V,E)be a graph,a function f:E→{-1,+1}is said to be a reverse signed total dominating function(RSTDF) of Gif ∑y∈Ntx]f(y)≤0 holds for eachx∈V∪E,where Nt(x)is the set of all elements which are adjacent to x or are incident to x,and is called the total neighbourhood of x,Ntx]=Nt(x)∪{x}is the closed one.The reverse signed total domination number of G is defined asγ′rst(G)=max{∑e∈V∪Ef(e)│f is a RSTDFofG}.In this paper,some upper bounds of the reverse signed total domination numbers of graphs are given,and determine the reverse signed total domination numbers of the cycles Cn. |
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| Keywords: | signed total dominating function signed total domination number reverse signed total dominating function reverse signed total domination number |
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