Ricci Curvature Formula: Applications to Bonnet-Myers Sharp Irregular Graphs
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866912129754333184 |
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| author | Li, Yupei Lu, Linyuan |
| author_facet | Li, Yupei Lu, Linyuan |
| contents | In this paper, we establish a simple formula for computing the Lin-Lu-Yau Ricci curvature on graphs. For any edge $xy$ in a simple locally finite graph $G$, the curvature $κ(x,y)$ can be expressed as a cost function of an optimal bijection between two blow-up sets of the neighbors of $x$ and $y$. Utilizing this approach, we derive several results including a structural theorem for the Bonnet-Myers sharp irregular graphs of diameter $3$ and a theorem on $C_3$-free Bonnet-Myers sharp graphs. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2409_15667 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Ricci Curvature Formula: Applications to Bonnet-Myers Sharp Irregular Graphs Li, Yupei Lu, Linyuan Combinatorics Differential Geometry 05C10, 53A70 In this paper, we establish a simple formula for computing the Lin-Lu-Yau Ricci curvature on graphs. For any edge $xy$ in a simple locally finite graph $G$, the curvature $κ(x,y)$ can be expressed as a cost function of an optimal bijection between two blow-up sets of the neighbors of $x$ and $y$. Utilizing this approach, we derive several results including a structural theorem for the Bonnet-Myers sharp irregular graphs of diameter $3$ and a theorem on $C_3$-free Bonnet-Myers sharp graphs. |
| title | Ricci Curvature Formula: Applications to Bonnet-Myers Sharp Irregular Graphs |
| topic | Combinatorics Differential Geometry 05C10, 53A70 |
| url | https://arxiv.org/abs/2409.15667 |