Lin-Lu-Yau curvature and diameter of amply regular graphs

Xintian Li, Shiping Liu

Published 2021-11-08, updated 2022-01-25Version 3

By Hall's marriage theorem, we study lower bounds of the Lin-Lu-Yau curvature of amply regular graphs with girth $3$ or $4$ under different parameter restrictions. As a consequence, we show that each conference graph has positive Lin-Lu-Yau curvature. Our approach also provides a geometric proof of a classical diameter estimate for amply regular graphs in the case of girth $4$ and some special cases of girth $3$.