Curvature and local matchings of conference graphs and extensions
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866910019438510080 |
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| author | Chen, Kaizhe Liu, Shiping Zhang, Heng |
| author_facet | Chen, Kaizhe Liu, Shiping Zhang, Heng |
| contents | We prove a conjecture of Bonini et al. on the precise values of the Lin--Lu--Yau curvature of conference graphs, i.e., strongly regular graphs with parameters $(4γ+1,2γ,γ-1,γ)$. Our method depends only on the parameter relations and applies to broader classes of amply regular graphs. In particular, we develop a new combinatorial approach to show the existence of local perfect matchings. A key observation is that counting common neighbors leads to useful quadratic polynomials. As a corollary, we derive an interesting number-theoretic result concerning quadratic residues. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2409_06418 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Curvature and local matchings of conference graphs and extensions Chen, Kaizhe Liu, Shiping Zhang, Heng Combinatorics Differential Geometry We prove a conjecture of Bonini et al. on the precise values of the Lin--Lu--Yau curvature of conference graphs, i.e., strongly regular graphs with parameters $(4γ+1,2γ,γ-1,γ)$. Our method depends only on the parameter relations and applies to broader classes of amply regular graphs. In particular, we develop a new combinatorial approach to show the existence of local perfect matchings. A key observation is that counting common neighbors leads to useful quadratic polynomials. As a corollary, we derive an interesting number-theoretic result concerning quadratic residues. |
| title | Curvature and local matchings of conference graphs and extensions |
| topic | Combinatorics Differential Geometry |
| url | https://arxiv.org/abs/2409.06418 |