Bonnet-Myers sharp graphs of diameter three

关于非正则 Bonnet-Myers 尖锐图的一个注记

A note on non-regular Bonnet-Myers Sharp Graphs

针对非自中心、非正则情形的分类难题，本文完整分类了直径为 2 的 Bonnet-Myers 尖锐图，并在对称反树族中构造出直径 3、4、6 的示例。

有向图上的施泰纳伯格曲率——离散的邦尼特 - 迈尔斯定理和利希纳罗维茨定理

Steinerberger Curvature On Digraphs -- Discrete Bonnet-Myers and Lichnerowicz Theorems

研究通过平衡测度编码图全局距离几何的施泰纳伯格曲率，推导二面体群和广义四元数群无向凯莱图的曲率公式，扩展到强连通简单有向图，建立其结构性质及相关定理。

Rigidity of the Bonnet-Myers inequality for graphs with respect to Ollivier Ricci curvature

We introduce the notion of Bonnet-Myers and Lichnerowicz sharpness in the Ollivier Ricci curvature sense. Our main result is a classification of all self-centered Bonnet-Myers sharp graphs (hypercubes, cocktail party graphs, even-dimensional demi-cubes, Johnson graphs $J(2n,n)$, the Gosset graph and suitable Cartesian products). We also present a purely combinatorial reformulation of this result. We show that Bonnet-Myers sharpness implies Lichnerowicz sharpness. We also relate Bonnet-Myers sharpness to an upper bound of Bakry-Émery $\infty$-curvature, which motivates a generalconjecture about…

Ricci曲率公式：在Bonnet-Myers尖锐不规则图中的应用

Ricci Curvature Formula: Applications to Bonnet-Myers Sharp Irregular Graphs

本文提出用最优双射代价函数计算图上Lin-Lu-Yau Ricci曲率的新公式，并借此刻画直径为3的Bonnet-Myers尖锐不规则图及无C3尖锐图的结构。

通过长尺度Ollivier Ricci曲率得到的距离正则图的直径界

Diameter bounds for distance-regular graphs via long-scale Ollivier Ricci curvature

本文利用长尺度Ollivier Ricci曲率与直径的关系，为距离正则图推导出新的锐利直径界，改进了离散Bonnet-Myers定理，并显著提升充分正则图及$(s,c,a,k)$-图的已有直径界。

Reflective Graphs, Ollivier curvature, effective diameter, and rigidity

We give a discrete Bonnet Myers type theorem for the effective diameter assuming positive Ollivier curvature. We prove that this diameter bound is attained if and only if the graph is a cocktail party graph, a Johnson graph, a halved cube, a Schläfli graph, a Gosset graph, or a cartesian product of the mentioned graphs with same Ollivier curvature. As a key step in the proof, we introduce the notion of reflective graphs as graphs such that for any two neighbors there exists a certain self-inverse automorphism mapping one neighbor to another. We classify these graphs as arbitrary cartesian prod…