2pqr阶的半对称图

Classifying and constructing graphs with given symmetric properties is a very important and active topic in algebraic graph theory. In this project, we investigate edge-transitive graphs, especially those graphs which are regular and not vertex-transitive, called semisymmetric graphs.Our main purpose is to classify semisymmetric graphs of order 2pqr under some condition and construct new examples. We mainly focus on these two problems: to give a classification of the semisymmetric graphs arising from quasiprimitive groups of degree pqr and a classification of locally primitive semisymmetric graphs of order 2pqr under non-quasiprimitive condition. For both of them, the key problem is to determine whether or not an edge-transitive graph is vertex-transitive.Therefore, to a great extent, one of our main tasks is to solve this problem under certain restrictions.

在代数图论中，构造和分类具有某种对称性质的图类是一个非常重要而且非常活跃的研究课题。本项目主要研究半对称图即边传递但不是点传递的正则图。主要目标是在一定限制条件下分类和刻画2pqr阶的半对称图。在本项目中，我们将主要解决两个问题，容许pqr次拟本原置换群的半对称图分类问题，和非拟本原情况下，对应阶数局部本原半对称图的分类问题。这两类问题的关键都是判断一个边传递图的自同构群是否在其点集上传递，因此，本项目从某种程度上说也就是在一定限制条件下解决上述问题。