半弧传递图与半边传递图的研究

项目名称： 半弧传递图与半边传递图的研究

项目编号： No.11201180

项目类型： 青年科学基金项目

立项/批准年度： 2013

项目学科： 数理科学和化学

项目作者： 王秀云

作者单位： 济南大学

项目金额： 22万元

中文摘要： 半弧传递图的研究是由Tutte在1966年提出的, 他证明了不存在奇数度半弧传递图。此后，半弧传递图的研究从不同的方面得到了广泛的研究，并且已经有很多重要的结论。我们主要从以下几个方面研究：四度半弧传递图的研究，主要解决无平方因子阶四度半弧传递图的分类；点本原半弧传递图的研究，主要包括确定本原半弧传递图的最小度数，以及一般度数本原半弧传递图的存在性问题等。 一个图称为半边传递图如果它的全自同构群作用在顶点集合上是传递的，作用在边集合和弧集合上都有两个长度相同的轨道。它是我们最近提出的一个新概念，需要进一步的探索。目前已知的非交换单群上An的四度非正规Cayley图都是半边传递图。自然地问题是：An上的四度非正规Cayley图是否都是半边传递图？这是我们研究半边传递图的主要原因。另外，在这方面我们希望给出半边传递图的一些性质特殊条件下的分类。

中文关键词： 半弧传递图；传递图；凯莱图；亚循环图；黑屋子图

英文摘要： In 1966 Tutte initiated an investigation of half-arc-transitive graphs by showing that a vertex- and edge-transitive graph with odd valency must be arc-transitive. Following the article, half-arc-transitive graphs have been extensively studied from different perpectives and there are many good results. We study the half-arc-transitive graphs on the following: the study of tetravalent half-arc-transitive graph; in this case, we want to determine the classification of the tetravalent half-arc-transitive graphs of order square-free. Primitive half-arc-transitive graph; in this case, we want to determine the smallest valency of the primitive half-arc-transitive graph and study the primitive half-arc-transitive graph with general valencies. A graph X is said to be the half-edge-transitive if its full automorphism group Aut(x) is transitive on the vertex set and has two orbits with the same length on the edge-set and arc-set. Half-arc-edge graph is a new idea, which is. Now, all known non-normal Cayley graphs on alternating groups An are half-edge-transitive graphs. A natural question is that whether tetralvalent non-normal Cayley graphs on alternating group An are half-edge-transitive graphs? This is why we therefore believe that the family of half-edge-transitive graphs is worth invedtigating. In this

英文关键词： half-arc-transitive graph；transitive graph；Cayley graph；Metacirculants；Heawood graph