Amply regular图的林-陆-丘曲率和直径

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

利用Hall匹配定理,研究了在不同参数限制条件下围长为3或4的amply regular图的林-陆-丘曲率下界估计.作为推论,我们证明每一个会议图均有正的林-陆-丘曲率.我们的方法在围长为4以及一些特殊的围长为3情形为amply regular图的一个经典直径估计提供了几何证明.

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 known diameter estimates of amply regular graphs in the case of girth 4 and some special cases of girth 3.