关于举行冯衍全教授（北京交通大学）学术报告会的通知

报告主题:    Graphical semiregular representation of finite group

报  告  人:    冯衍全 教授

报告时间:    2024年 5月16日（星期四）下午15:00-16:00

报告地点:    腾讯会议：361-233-901

邀  请  人:    林鸿莺副教授

欢迎广大师生前往！

数学学院

2024年5月15日

报告摘要：A digraph or a graph $\Gamma$ is called a {\em digraphical or graphical

regular representation} (DRR or GRR for short) of a group $G$ respectively, if ${\rm Aut}(\Gamma)\cong G$ is regular on the vertex set $V(\Gamma)$. A group $G$ is called a DRR group or a GRR group if there is a digraph or a graph $\Gamma$ such that $\Gamma$ 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 {\em digraphical or graphical $m$-semiregular representation} of $G$, that is, a regular digraph or a graph $\Gamma$ such that ${\rm Aut}(\Gamma)\cong G$ is semiregular on $V(\Gamma)$ 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.

报告人介绍：冯衍全，北京交通大学二级教授，自1997年获北京大学理学博士学位以来，一直从事代数与组合，群与图以及互连网络方面研究。现任中国工业与应用数学学会理事、中国数学会理事等，代数组合JACO等杂志编委。2010年主持《图的对称性》获教育部优秀成果二等奖，2011年获政府特殊津贴。共发表SCI科研论文150余篇，主持完成国家自然科学基金10余项，包括重点项目1项。正在承担国家自然科学基金重点项目1项、面上项目1项、国际合作研究项目1项。