| 关于最小度至少为3的图的全控制数 |
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| 引用本文： | 刘海龙,孙良.关于最小度至少为3的图的全控制数[J].北京理工大学学报(英文版),2002,11(2):217-219. |
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| 作者姓名： | 刘海龙 孙良 |
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| 作者单位： | 北京理工大学,应用数学系,北京,100081 |
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| 摘 要： | 设G是一个没有孤立点的简单图.G的顶点集的一个子集S是一个全控制集,如果G的每个顶点都相邻于S中的某个顶点.图G的全控制数,用γt(G)来表示,是G的全控制集中的顶点数最少的全控制集的顶点数.证明了如果G是一个最小度至少为3的图,那么γt(G)≤n/2.从而证明了Favaron, Henning, Mynhart和Puech提出的一个猜想成立.
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| 关 键 词： | 简单图 控制 全控制 |
| 收稿时间： | 2001/6/20 0:00:00 |
On the Total Domination Number of Graphs with Minimum Degree at Least Three |
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| LIU Hai long and SUN Liang.On the Total Domination Number of Graphs with Minimum Degree at Least Three[J].Journal of Beijing Institute of Technology,2002,11(2):217-219. |
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| Authors: | LIU Hai long and SUN Liang |
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| Affiliation: | Department of Applied Mathematics, Beijing Institute of Technology, Beijing100081, China;Department of Applied Mathematics, Beijing Institute of Technology, Beijing100081, China |
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| Abstract: | Let G be a simple graph with no isolated vertices. A set S of vertices of G is a total dominating set if every vertex of G is adjacent to some vertex in S. The total domination number of G, denoted by γt(G), is the minimum cardinality of a total dominating set of G. It is shown that if G is a graph of order n with minimum degree at least 3, then γt(G)≤n/2. Thus a conjecture of Favaron, Henning, Mynhart and Puech is settled in the affirmative. |
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| Keywords: | simple graph domination total domination |
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