循环完全图K(7m,7)的自同态幺半群 Alternative Title The endomorphism monoids of circulant complete graphs K(7m,7) 韩斌 Thesis Advisor 罗彦锋 2015-06-01 Degree Grantor 兰州大学 Place of Conferral 兰州 Degree Name 硕士 Keyword 循环完全图 自同态 自同态幺半群 自同态型 自同态谱 Abstract 图的自同态幺半群将图论理论和半群代数理论联系起来, 是代数图论研究中的一个主要课题.本文主要利用循环完全图K(7m,7)的组合结构来研究其自同态幺半群的代数结构和性质.本文分为两章，第一章介绍了相关的研究背景和预备知识.第二章主要研究K(7m,7)的自同态幺半群的结构, 验证了K(7m,7)的的自同态幺半群的正则性, 而且证明了K(7m,7)的自同态幺半群不是纯整半群, 刻画了K(7m,7)的自同构群, 得到了它的自同态型和自同态谱, 并且解决了其自同态幺半群的计数问题. Other Abstract Graphs and their endomorphism monoid,which are the connection between the graph theory and semigroup algebraic theory, are the main research subject of algebraic graph theory.this dissertation.The main research contents are to study the algebraic structures and properties of endomorphism monoid of circulant complete graph K(7m,7) with the combination structures of graphs.There are two chapters in this paper.The first chapter gives the study background. The second chapter mainly studies the endomorphism monoid structure of K(7m,7).The endomorphism monoids of the graph K(7m,7)are regular will be certified, and the endomorphism monoids of K(7m,7) are not orthodox semigroup,the automorphism group of K(7m,7)will be depicted.Its endomorphism type and endomorphism spectrum will be obtained,and its enumeration problems of endomorphism monoids will be resolved. URL 查看原文 Language 中文 Document Type 学位论文 Identifier https://ir.lzu.edu.cn/handle/262010/224550 Collection 数学与统计学院 Recommended CitationGB/T 7714 韩斌. 循环完全图K(7m,7)的自同态幺半群[D]. 兰州. 兰州大学,2015.
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