| 强乘积图与字典乘积图的控制数 |
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| 引用本文： | 赵维胜,欧见平. 强乘积图与字典乘积图的控制数[J]. 五邑大学学报(自然科学版), 2010, 24(3): 7-9 |
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| 作者姓名： | 赵维胜 欧见平 |
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| 作者单位： | 五邑大学,数学与计算科学学院,广东,江门,529020 |
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| 基金项目： | 国家自然科学基金资助项目，广东省自然科学基金资助项目 |
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| 摘 要： | 证明了:1)图G和H的强乘积图GH的控制数γ(GH)≤γ(G)γ(H),并举例说明此上界是可以达到的;2)若γ(H)=1,则G与H的字典乘积图的控制数γ(G H)=γ(G);若G不含孤立点并且γ(H)≥2,则γ(G H)=γt(G),其中γt表示图的全控制数.
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| 关 键 词： | 强乘积图 字典乘积图 控制数 全控制数 |
Domination Numbers of Strong Products and Lexicographic Products of Graphs |
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| ZHAO Wei-sheng,OU Jian-ping. Domination Numbers of Strong Products and Lexicographic Products of Graphs[J]. Journal of Wuyi University(Natural Science Edition), 2010, 24(3): 7-9 |
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| Authors: | ZHAO Wei-sheng OU Jian-ping |
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| Affiliation: | (School of Mathematics and Computational Science,Wuyi University,Jiangmen 529020,China) |
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| Abstract: | It is proved in this paper that the domination number of the strong product of graphs G and H is upper bounded by γ（GH） ≤γ（G）γ（H）,and this bound is proved by examples to be reachable.If γ（H） = 1,then the domination number of the lexicographic product of graphs G and H is γ（GοH） = γ（G）;and if G contains no isolated vertex and γ（H） ≥ 2,then γ（GοH）= γ t（G）,where γ t is the total domination number. |
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| Keywords: | strong product graph lexicographic product graph domination number total domination number |
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