若干传递图类及其相关问题研究

项目名称： 若干传递图类及其相关问题研究

项目编号： No.11461077

项目类型： 地区科学基金项目

立项/批准年度： 2015

项目学科： 数理科学和化学

项目作者： 潘江敏

作者单位： 云南财经大学

项目金额： 36万元

中文摘要： 本项目计划研究若干重要的传递图类及其关联的置换群问题：（1）分类包含传递亚循环子群的二部拟本原置换群和顶点二部拟本原边传递亚循环图，刻画其他重要的亚循环图子类；（2）刻画非交换单群上素数度弧传递凯莱图的正规性和正则性以及相关的群的因子分解问题；(3) 研究一些重要的对称图无穷类的弧传递正则覆盖；（4）刻画包含传递交换子群的非本原置换群和交换群上的弧传递凯莱图；（5）刻画立方自由阶点传递局部本原图；（6）其他相关问题。 以上课题都是代数图论和置换群领域的重要问题，其中亚循环图问题、正则覆盖问题、包含传递子群的置换群问题、群的因子分解问题等都是非常基本和深刻的，它们的研究结果将会推动相关理论的发展，对研究其它许多问题产生重要影响。 本项目的主要预期成果为高水平的研究论文，预期在SCI源刊和核心刊物上发表论文15篇左右。

中文关键词： 凯莱图；亚循环图；融合；正则覆盖；单群

英文摘要： This project proposed to study certain important families of transitive graphs and related problems in the field of permutation group theory. (1) Classifying biquasiprimitive permutation groups containing a transitive metacyclic subgroup and vertex biquasiprimitive edge transitive metacirculants, and characterizing certain subclasses of metacircualnts; (2) Characterizing arc transitive Cayley graphs with prime valency of nonabelian simple groups and relative factorization problems of certern groups; (3) Studying acr transitive regular coverings of certain typical infinite families of symmetric graphs; (4) Characterizing certern classes of imprimitive permutation groups containing a transitive subgroup and arc transitive abelian Cayley graphs; (5) Characerizing vertex transitive locally primitive graphs of cube free order; (6) Other corresponding problems. The above topics are important in the field of algebraic graph theory and permutation group theory, and among them，metacirculant problem, regular cover problem, permtutation groups with a transitive subgroup and factorization s of groups etc. are fundamental and deep. The results obtained on these topics will improve the corresponding theory, and produce significant affects on many other problems. The main expected results of the project are high quality research papers, including about 15 papers on SCI source journals.

英文关键词： Cayley graph;metacirculant;amalgam;regular cover;simple group