讲座主题：Existence of non-Cayley Haar graphs

主讲人： 杨大伟

工作单位：北京邮电大学

活动时间：2020年12月13日 14:50-15:40

讲座地点：腾讯会议，会议ID：850 153 808

主办单位：烟台大学数学与信息科学学院

内容摘要：

A Cayley graph of a group H is a finite simple graphΓsuch that its automorphism group Aut(Γ) contains a subgroup isomorphic to H acting regularly on V(Γ), while a Haar graph of H is a finite simple bipartite graphΣsuch that Aut(Σ) contains a subgroup isomorphic to H acting semiregularly on V(Σ) and the H-orbits are equal to the partite sets ofΣ. It is well-known that every Haar graph of finite abelian groups is a Cayley graph. In this paper, we prove that every finite non-abelian group admits a non-Cayley Haar graph except the dihedral groups D6, D8, D10, the quaternion group Q8 and the group Q8×Z2. This answers an open problem proposed by Estelyi and Pisanski in 2016. This is joint work with Yan-Quan Feng, Istvan Kovacs and Jie Wang.

主讲人介绍：

杨大伟，理学博士，北京邮电大学讲师。研究方向为代数图论、图论与网络，主要研究内容为图与网络的对称性，网络的嵌入与容错性分析等。目前已在European J. Combin., J. Algebraic Combin., Inform. Sci.等国际期刊发表十余篇学术论文，主持或参与多项省部级以上科研项目。