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arXiv · 2409.06418

Curvature and local matchings of conference graphs and extensions

Kaizhe Chen·Shiping Liu·Heng Zhang
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Abstract

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.

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Kaizhe Chen, Shiping Liu, Heng Zhang. 2026-02-12. Curvature and local matchings of conference graphs and extensions. https://arxiv.org/abs/2409.06418

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