论文标题
反射图，圆润曲率，有效直径和刚度
Reflective Graphs, Ollivier curvature, effective diameter, and rigidity
论文作者
论文摘要
我们给出一个离散的引擎盖Myers型定理，以实现有效直径，假设呈阳性曲率。我们证明，当且仅当图形是鸡尾酒会图，约翰逊图，一半的立方体，schläfli图，棉图图或带有相同易感曲率的上述图的笛卡尔产物时，我们才能实现这种直径结合。作为证明的关键步骤，我们将反射图的概念介绍为图形，以使任何两个邻居都存在某种自身隔离的自动形态，将一个邻居映射到另一个邻居。我们将这些图表分类为前面提到的图形的任意笛卡尔产品。
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 products of the graphs mentioned before.
