半群的Cayley图与tao图的若干研究 Alternative Title Studies on Caley graphs and tao graphs of semigroups 杨东 Thesis Advisor 罗彦锋 2011-06-03 Degree Grantor 兰州大学 Place of Conferral 兰州 Degree Name 博士 Keyword Cayley图 单演半群 矩形带 正规带 左群 群 点可迁性 可扩性 Abstract 半群的图的研究是代数图论近年来一个十分活跃的研究领域，本文推广了半群的图的概念，引入了半群的图，研究了半群的图和图的结构和性质。 设是一个半群，是的两个子集，且中至少有一个是非空集合。称一个有向图为的图，记为，如果， ，当时，的就是的除图；当时，的就是的关于联络集的图。 首先, 我们通过半群的图研究了半群的一个组合性质：-饱和性, 其中是一个有限图。给出了半群是D-饱和的的充分必要条件，不但推广了和关于半群是图-饱和的的工作，而且解决了半群什么时候是除图-饱和的的问题。 其次我们刻画了完全单的周期半群的图的点可迁性，得到了完全单的周期半群的图是-点可迁的，-点可迁的，以及 -点可迁的的充分必要条件。描述了单演半群、矩形带、 正规带、左群及群等一些特殊的半群类的图的结构和性质，也研究了一般半群的图,得到了若干性质,包括给出了图是-点可迁的必要条件。 最后我们研究了偶数阶群的拟交换图的匹配可扩性,给出了偶数阶群的拟交换图是2--可扩的完全刻画。 Other Abstract The research on Cayley graphs of semigroups is an active scientific field in recent years. In this thesis we define a graph: a generalization of the Cayley graph of semigroup and do some researches on structure and properties of Cayley graphs and graphs. Let S be a semigroup and subsets of S. Suppose that either or . A directed graph is defined as graph, denoted by, of S , if V()=S, for some.In particular, in case of T1=T2=S, the graph of S is exactly the divisibility graph Div(S); in case of ,the graph of S is exactly the Cayley graph Cay(S,T1) of S relative toT1. Firstly, we study the D-saturation about semigroups by the graphs of semigroups, where D is a finite graph, and give some necessary and sufficient conditions for semigroups beingD-saturated. The results not only generalize ones on D-saturation of Cayley graphs of semigroups obtained by A.V.Kelarev and S.J. Quinn, but also give the conditions of semigroups being Div(S) D-saturated. Secondly we characterize the vertex-transitive properties of Cayley graphs of completely simple periodic semigroups, obtain necessary and sufficient conditions for Cayley graphs of completely simple Pe- riodic semigroups being ColAutS-vertex-transitive, EndS-vertex-transitive and ColEndS(G)–vertex-tran- sitive, respectively, give not only structure and properties of graphs of such special semigroups as monogenic semigroups, rectangular bands, normal bands, left groups and groups, but also some properties of general semigroups, including the necessary conditions for graphs of semigroups being ColEnd()-vertex-transitive. Finally, we study the property of match extendability of quasi-abelian Cayley graphs of groups with even order and give a complete characterization for 2-extendability of quasi-abelian Cayley graphs of groups with even order. URL 查看原文 Language 中文 Document Type 学位论文 Identifier https://ir.lzu.edu.cn/handle/262010/225627 Collection 数学与统计学院 Recommended CitationGB/T 7714 杨东. 半群的Cayley图与tao图的若干研究[D]. 兰州. 兰州大学,2011.
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