Graphical semiregular representation of finite group
数学专题报告
报告题目(Title)：Graphical semiregular representation of finite group
报告人(Speaker)：冯衍全教授 （北京交通大学）
地点(Place)：后主楼1124
时间(Time)：2023 年 11 月 2 日（周四） 16:00--17:00
邀请人(Inviter)：徐敏
报告摘要
A digraph or a graph G is called a digraphical or graphical regular representation (DRR or GRR for short) of a group G respectively, if Aut(G) ≅ G is regular on the vertex set V(G). A group G is called a DRR group or a GRR group if there is a digraph or a graph G such that G 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 G such that Aut(G) ≅ G is semiregular on V(G) 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.
主讲人简介
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。
