无四边形的非负 Bakry-Émery 曲率图形

arXiv - MATH - Metric Geometry Pub Date : 2024-08-19 DOI:arxiv-2408.09823

Huiqiu Lin, Zhe You

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摘要

Lin和Yau[\emph{Math. Res.Lett.}, 2010]引入了基于曲率维条件的Bakry-\'Emery意义上的图的里奇曲率定义。Hua 和 Lin [\emph{Comm. Anal. Geom.}，2019] 对满足曲率维条件 $CD(0,\infty)$、周长至少为五的无权重图进行了分类。本文分类了所有满足曲率维度条件$CD(0,\infty)$的最小阶数至少为2的无连接无权重归一化$C_4$无图，以及无阶数条件的非归一化拉普拉斯图...

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Graphs with nonnegative Bakry-Émery curvature without Quadrilateral

The definition of Ricci curvature on graphs in Bakry-\'Emery's sense based on curvature dimension condition was introduced by Lin and Yau [\emph{Math. Res. Lett.}, 2010]. Hua and Lin [\emph{Comm. Anal. Geom.}, 2019] classified unweighted graphs satisfying the curvature dimension condition $CD(0,\infty)$ whose girth are at least five. In this paper, we classify all of connected unweighted normalized $C_4$-free graphs satisfying curvature dimension condition $CD(0,\infty)$ for minimum degree at least 2 and the case with non-normalized Laplacian without degree condition..

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arXiv - MATH - Metric Geometry

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