项目名称: 一些传递图类及其相关问题的研究
项目编号: No.11301484
项目类型: 青年科学基金项目
立项/批准年度: 2014
项目学科: 数理科学和化学
项目作者: 刘哲
作者单位: 浙江农林大学
项目金额: 22万元
中文摘要: 传递图是代数图论的基本研究对象,在包括生物科学、计算机科学、编码理论等学科都有十分重要的应用。本项目将研究一些重要的传递图类及其相关问题,拟研究的主要课题为:(1)研究立方自由阶素数度的1-弧正则图,特别的,刻画立方自由阶3度和5度对称图;(2)研究立方自由阶2-弧传递Cayley图;(3)刻画立方自由阶的度数不超过10的core-free弧传递Cayley图;(4)研究立方自由阶有限群的自同构群,并刻画立方自由阶素数度弧传递正规Cayley图;(5)其它相关问题。 本项目预期对以上多个课题得到较完备的刻画。
中文关键词: 弧传递图;自同构群;覆盖;自补图;亚本原置换群
英文摘要: Transitive graphs are the fundamental research objects of the algebraic graph theory, and have very important applications in the subjects including biological science, computer science and code science, etc. This project aims to study some important families of transitive graphs and certain relative problems, stated as following: (1) Characterizing arc transitive graphs of cube-free order of prime valency; especially, characterise cubic and pentavalent symmetric graphs of cube-free order; (2) Studying 2 arc-transitive of cube-free order; (3) Classifying core-free cayley arc-transitive graphs of cube-free order whose valency at most 10; (4) Studying automorsim groups of groups of cube free order, and classifying arc transitve Cayley normal graphs of cube-free order of prime valency; (5) Certain Relative problems. This project except to obtain some complete characterization of most topics stated above.
英文关键词: arc-transitive graphs;automorphism groups;cover;self-complementary graphs;meta-primitive groups