论文标题
通过lin-lu-yau曲率界定正规图的直径和特征值
Bounding the diameter and eigenvalues of amply regular graphs via Lin-Lu-Yau curvature
论文作者
论文摘要
充分的常规图是一个常规图，以使任何两个相邻的顶点都有$α$ common邻居，并且任何两个具有距离$ 2 $的顶点都有$β$ $β$共同的邻居。我们证明了lin-lu-yau曲率的急剧下限估计值，带有周长$ 3 $和$β>α$的任何正规图。证明涉及将离散的RICCI曲率与局部匹配属性有关的新想法：这包括从局部结构和相关距离估计值的常规两部分图的新结构。结果，我们获得了适当的常规图的尖锐直径和特征值边界。
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 proof involves new ideas relating discrete Ricci curvature with local matching properties: This includes a novel construction of a regular bipartite graph from the local structure and related distance estimates. As a consequence, we obtain sharp diameter and eigenvalue bounds for amply regular graphs.
