| 图的弱自同态幺半群 |
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| 引用本文： | 侯海龙,董文瑾,谷蕊.图的弱自同态幺半群[J].河南科技大学学报(自然科学版),2012(1):75-77,9. |
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| 作者姓名： | 侯海龙 董文瑾 谷蕊 |
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| 作者单位： | 河南科技大学数学与统计学院;兰州大学数学与统计学院 |
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| 基金项目： | 国家自然科学基金项目(10971053);河南省教育厅基金项目(2009A110005) |
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| 摘 要： | 定义了图的弱自同态,证明了一个图的所有弱自同态在映射的合成下可以构成一个幺半群,刻画了图的弱自同态幺半群的两类格林关系(L关系和R关系)。通过L关系给出了其每个L类中都包含幂等元的条件。最后,给出了图的弱自同态幺半群是正则半群的充分必要条件。
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| 关 键 词： | 弱自同态 格林关系 正则半群 |
Weak Endomorphism Monoid of a Graph |
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| HOU Hai-Long,DONG Wen-Jin,GU Rui.Weak Endomorphism Monoid of a Graph[J].Journal of Henan University of Science & Technology:Natural Science,2012(1):75-77,9. |
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| Authors: | HOU Hai-Long DONG Wen-Jin GU Rui |
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| Institution: | 1(1.Mathematics & Statistics School,Henan University of Science & Technology,Luoyang 471003,China;2.School of Mathematics & Statistics,Lanzhou University,Lanzhou 730000,China) |
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| Abstract: | In this paper,the weak endomorphism of a graph was defined.It is proved that the set of all weak endomorphisms of a graph can form a monoid.The Green ’ s relation of these monoids is described.The conditions are given under which every L-class of the weak endomorphism monoid of a graph contains a idempotent.The conditions are got under which the weak endomorphism monoid of a graph is regular. |
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| Keywords: | Weak endomorphism Green’s relation Regular semigroup |
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