Diamater and connectivity of amply regular graphs via Ricci curvature

23.04.2025, 13:00  –  Haus 9, Raum 0.17 und Zoom
Forschungsseminar Diskrete Spektraltheorie

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.