边传递Cayley图的对称性研究
发布时间：2018-12-31 09:36
【摘要】：图的对称性研究是一个比较活跃的研究领域,其主要研究对象是点传递图、边传递图等具有较高对称性质的图.研究某种具有对称性质的图有重要的理论意义.在图的对称性研究中,确定图的自同构群是具有基本重要性的工作.如果图的自同构群在图的顶点集、边集或2-弧集上作用传递,则称图分别为点传递的、边传递的或2-弧传递的.本文的主要研究对象是具有边传递性质的Cayley图.本文的主要工作是研究无平方因子阶的局部本原图和本原2-弧传递图的对称性.首先,本文通过考察图的自同构群某个最大正规子群在其顶点集上的轨道情况,得到了无平方因子阶局部本原图及其自同构群的简单刻画.其次,本文通过对有限群的子群结构和图自同构群的点稳定子分析,构造满足条件的相关图类,得到了无平方因子阶本原2-弧传递图的分类与刻画。
[Abstract]:The symmetry study of graphs is an active research field. The main research objects are vertex transitive graphs, edge transitive graphs and other graphs with higher symmetry. It is of great theoretical significance to study some graphs with symmetric properties. In the study of graph symmetry, determining the automorphism group of graphs is of fundamental importance. If the automorphism group of a graph is transitive on the vertex set, edge set or 2-arc set of a graph, then the graph is point-transitive, edge-transitive or 2-arc transitive, respectively. The main research object of this paper is Cayley graph with edge transitive property. The main work of this paper is to study the symmetry of local primitive graphs and primitive 2-arc transitive graphs of square free order. Firstly, by investigating the orbit of a maximal normal subgroup on the vertex set of a graph, we obtain a simple characterization of the square free order local primitive graph and its automorphism group. Secondly, by analyzing the subgroup structure of finite groups and the vertex stability subgroups of graph automorphism groups, we construct the classes of correlation graphs satisfying the conditions, and obtain the classification and characterization of primitive 2-arc transitive graphs of square free order.
【学位授予单位】：安徽工业大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：O157.5
[Abstract]:The symmetry study of graphs is an active research field. The main research objects are vertex transitive graphs, edge transitive graphs and other graphs with higher symmetry. It is of great theoretical significance to study some graphs with symmetric properties. In the study of graph symmetry, determining the automorphism group of graphs is of fundamental importance. If the automorphism group of a graph is transitive on the vertex set, edge set or 2-arc set of a graph, then the graph is point-transitive, edge-transitive or 2-arc transitive, respectively. The main research object of this paper is Cayley graph with edge transitive property. The main work of this paper is to study the symmetry of local primitive graphs and primitive 2-arc transitive graphs of square free order. Firstly, by investigating the orbit of a maximal normal subgroup on the vertex set of a graph, we obtain a simple characterization of the square free order local primitive graph and its automorphism group. Secondly, by analyzing the subgroup structure of finite groups and the vertex stability subgroups of graph automorphism groups, we construct the classes of correlation graphs satisfying the conditions, and obtain the classification and characterization of primitive 2-arc transitive graphs of square free order.
【学位授予单位】：安徽工业大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：O157.5
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相关期刊论文 前6条
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