| 一类循环完全图的自同态幺半群 |
| Alternative Title | The endomorphism monoids of a certain class of circulant complete graphs
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| 刘书琛 |
| Thesis Advisor | 罗彦锋
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| 2014-06-07
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| Degree Grantor | 兰州大学
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| Place of Conferral | 兰州
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| Degree Name | 硕士
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| Keyword | 循环完全图
自同态型
自同态谱
自同态幺半群
自同态正则
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| Abstract | 图及其自同态幺半群属于图论和半群代数理论的交叉领域, 是代数图论的一个重要的研究方向,
它主要研究图的组合结构和自同态幺半群的代数结构和性质,
以及二者之间的联系. 通过对图的自同态及自同态幺半群的研究, 不仅丰富了图论和半群代数理论的研究内容,
而且将促进二者的融合与发展.
本文主要研究循环完全图K(6m,6)的自同态及自同态幺半群, 证明了K(6m,6)的自同态幺半群是正则的, 确定了K(6m,6)的自同构群, 给出了它的自同态谱和自同态型, 解决了其自同态幺半群的计数问题. |
| Other Abstract | Graphs and their endomorphism monoids, which belong to interdisciplinary of graph theory and semigroup algebraic theory, are the important research direction of algebraic graph theory. The main research contents are to study the combination structures of graphs, the algebraic structures and properties of endomorphism monoids, and to consider the connection between them. The researches on endomorphism of graphs and their endomorphism monoids will not only enrich the research contents of graph theory and the theory of semigroups, but also play an active role in promoting the intersection and merging of algebra with other discipline areas.
In this dissertation, the endomorphism of circulant complete graphK(6m,6)and their endomorphism monoids will be studied. The endomorphisms monoid of the graphK(6m,6)$is regular will be proved,
the automorphism group ofK(6m,6)will be determined, its endomorphism spectrum and endomorphism type will be shown, and its enumeration problems of endomorphism monoids will be solved. |
| URL | 查看原文
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| Language | 中文
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| Document Type | 学位论文
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| Identifier | https://ir.lzu.edu.cn/handle/262010/224440
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| Collection | 数学与统计学院
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Recommended Citation
GB/T 7714 |
刘书琛. 一类循环完全图的自同态幺半群[D]. 兰州. 兰州大学,2014.
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