中国科学技术大学学报 ›› 2021, Vol. 51 ›› Issue (12): 889-893.DOI: 10.52396/JUST-2021-0232

• 研究论文 • 上一篇    下一篇

Amply regular图的林-陆-丘曲率和直径

李心田, 刘世平*   

  1. 中国科学技术大学数学科学学院,安徽合肥 230026
  • 收稿日期:2021-11-09 修回日期:2021-11-16 出版日期:2021-12-31 发布日期:2022-01-11
  • 通讯作者: *E-mail:spliu@ustc.edu.cn

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

LI Xintian, LIU Shiping*   

  1. School of Mathematical Sciences, University of Science and Technology of China, Hefei 230026, China
  • Received:2021-11-09 Revised:2021-11-16 Online:2021-12-31 Published:2022-01-11
  • Contact: *E-mail: spliu@ustc.edu.cn

摘要: 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.

关键词: amply regular 图, 完美匹配, 最优传输距离, 林-陆-丘曲率

Abstract: 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.

Key words: amply regular graph, perfect matching, Wasserstein distance, Lin-Lu-Yau curvature

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