Bounding the diameter and eigenvalues of amply regular graphs via Lin-Lu-Yau curvature

An amply regular graph is a regular graph such that any two adjacent vertices have $α$ common neighbors and any two vertices with distance $2$ have $β$ common neighbors. We prove a sharp lower bound estimate for the Lin--Lu--Yau curvature of any amply regular graph with girth $3$ and $β>α$. The proo