讲座主题：Graphical semiregular representation of finite group

专家姓名：冯衍全

工作单位：北京交通大学

讲座时间：2023年04月13日15:00-16:00

讲座地点：数学院三楼会议室

主办单位：hy590海洋之神平台数学与信息科学学院

内容摘要：

A digraph or a graph Γ is called a digraphical or graphical regular representation (DRR or GRR for short) of a group G respectively, if Aut(Γ) is regular on the vertex set V(Γ). A group G is called a DRR group or a GRR group if there is a digraph or a graph Γ such that Γ is a DRR or GRR of G. Babai and Godsil classified finite DRR groups and GRR groups in 1980 and 1981, respectively. Then a lot of variants relative to DRR or GRR, with some restrictions on (di)graphs or groups, were investigated by many researchers. We extend regular representation to semiregular representation. For a positive integer m, a group G is called a DmSR group or a GmSR group, if there is a digraphical or graphical m-semiregular representation of G, that is, a regular digraph or a graph Γ such that Aut(Γ) is semiregular on V(Γ) with m orbits. Clearly, D1SR and G1SR groups are the DRR and GRR groups. In this talk, we review some progress on DmSR groups and GmSR groups for all positive integer m, and their variants by restricting (di)graphs or groups.

主讲人介绍：

冯衍全，北京交通大学二级教授，政府特殊津贴获得者，获教育部自然科学二等奖。从事群、图及互连网络研究工作，在Journal of Combinatorial Theory, Series A、Journal of Combinatorial Theory, Series B、Journal of Algebra等国际著名期刊上发表学术论文150篇。主持完成国家自然科学基金10余项，目前主持国家自然科学基金重点项目1项、国际合作研究项目2项。担任国际代数组合权威期刊Journal of Algebraic Combinatorics等编委，担任中国数学会理事、中国工业与应用数学学会理事、中国运筹学会图论组合学分会常务理事等。