Classifications of graphical m-semiregular representation of finite groups

报告题目：Classifications of graphical m-semiregular representation of finite groups

报告人：  冯衍全教授

报告时间：2021年10月9号16：30

报告地点：마카오 슬롯 머신 잭팟A302

报告人简介： 冯衍全，北京交通大学二级教授，多年来一直从事代数与组合、群与图以及网络理论研究。目前担任中国工业与应用数学学会常务理事、中国数学会理事、中国运筹学会图论组合学分会常务理事。2010年主持《图的对称性》获教育部自然科学二等奖，2011年获政府特殊津贴。被邀请到国外著名大学进行合作研究五十余次，多次在国内外重要学术会议上作大会邀请报告，多次组织国际学术会议，如2021年组织第8届欧洲数学家大会《群、图与网络》专题会议、2014年8月在北京交通大学组织国际数学家大会《组合与图论国际会议》卫星会议。主持完成国家自然科学基金、政府间科技合作、博士点基金等10余项，正在主持国家自然科学基金重点项目1项。共发表高水平科研成果100余篇，其中在组合顶级刊物JCTA/B上12篇，图论顶级刊物JGT上6篇, 代数组合顶级刊物JACO上7篇，代数顶级刊物JA上1篇，群论顶级刊物JGT上2篇，欧洲组合EJC上13篇等。2021年入选中国高被引学者榜单。代数图论顶级刊物JACO和重要刊物《Ars Mathematica Contemporanea》编委

报告摘要：A graph or digraph is called regular if each vertex has the same valency, or, the same out-valency and the same in-valency, respectively. Recently, we extend the classical notion of digraphical and graphical regular representation of a group.

A (di)graphical m-semiregular representation(respectively, GmSR and DmSR, for short) of a group G is a regular (di)graph whose automorphism group is isomorphic to G and acts semiregularly on the vertex set with m orbits. When m=1, this definition agrees with the classical notion of GRR and DRR. Finite groups admitting a D1SR were classified by Babai in 1980, and the analogue classification of finite groups admitting a G1SR was completed by Godsil in 1981. Pivoting on these two results, we classify finite groups admitting a GmSR or a DmSR (for arbitrary positive integers m) and also do some work about bipartite (di)graphs.