The edge-connectivity of strongly 3-walk-regular graphs
报告题目(Title)：The edge-connectivity of strongly 3-walk-regular graphs
报告人(Speaker)：冯荣权 教授 （北京大学）
地点(Place)：腾讯会议 746 166 009
时间(Time)：2020年6月8日 15：30-16：30
邀请人(Inviter)：王恺顺
报告摘要
E.R. van Dam and G.R. Omidi generalized the concept of strongly regular graphs to strongly 3-walk-regular graphs such that for any two vertices the number of `-walks (walks of length `) from one vertex to the other is the same which depends only on whether the two vertices are the same, adjacent or non-adjacent. In this talk, we proved that the edge-connectivity of a connected strongly 3-walk-regular graph G of degree k 3 is equal to k. Moreover, if G is not the graph formed by adding a perfect matching between two copies of K4, then each edge cut set of size k is precisely the set of edges incident with a vertex of G. Furthermore, for a regular graph G in general, we also give a sufficient and tight condition such that G is 1-extendable.
