Diameter bounds for distance-regular graphs via long-scale Ollivier Ricci curvature
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866908509040279552 |
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| author | Chen, Kaizhe Liu, Shiping |
| author_facet | Chen, Kaizhe Liu, Shiping |
| contents | In this paper, we derive new sharp diameter bounds for distance regular graphs, which better answer a problem raised by Neumaier and Penji\' c in many cases. Our proof is built upon a relation between the diameter and long-scale Ollivier Ricci curvature of a graph, which can be considered as an improvement of the discrete Bonnet-Myers theorem. Our method further leads to significant improvements of existing diameter bounds for amply regular graphs and $(s,c,a,k)$-graphs. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2412_18480 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Diameter bounds for distance-regular graphs via long-scale Ollivier Ricci curvature Chen, Kaizhe Liu, Shiping Combinatorics In this paper, we derive new sharp diameter bounds for distance regular graphs, which better answer a problem raised by Neumaier and Penji\' c in many cases. Our proof is built upon a relation between the diameter and long-scale Ollivier Ricci curvature of a graph, which can be considered as an improvement of the discrete Bonnet-Myers theorem. Our method further leads to significant improvements of existing diameter bounds for amply regular graphs and $(s,c,a,k)$-graphs. |
| title | Diameter bounds for distance-regular graphs via long-scale Ollivier Ricci curvature |
| topic | Combinatorics |
| url | https://arxiv.org/abs/2412.18480 |