Kaizhe Chen (Hefei, China)
Abstract: A d-regular graph is called amply regular if there are constants α,β such that any two adjacent vertices have α commom neighbors and any two vertices at distance 2 have β commom neighbors. Through calculations of Lin-Lu-Yau curvature and Bakry-Emery curvature, we obtain new diameter bounds for amply regular graphs, which make a progress on several related conjectures. Moreover, we explore the interaction between connectivity and Lin-Lu-Yau curvature. Consequently, we estimate or determine the connectivity and edge-connectivity of amply regular graphs.
