Graphs with nonnegative Bakry-Émery curvature without Quadrilateral
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arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866909290610032640 |
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| author | Lin, Huiqiu You, Zhe |
| author_facet | Lin, Huiqiu You, Zhe |
| contents | The definition of Ricci curvature on graphs in Bakry-Émery'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.. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2408_09823 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Graphs with nonnegative Bakry-Émery curvature without Quadrilateral Lin, Huiqiu You, Zhe Combinatorics Metric Geometry 05C99, 51F99 The definition of Ricci curvature on graphs in Bakry-Émery'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.. |
| title | Graphs with nonnegative Bakry-Émery curvature without Quadrilateral |
| topic | Combinatorics Metric Geometry 05C99, 51F99 |
| url | https://arxiv.org/abs/2408.09823 |