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arXiv · 2610.24716

Planar graphs whose second largest eigenvalue does not exceed 1

Zihao Geng·Zhiwen Wang·Wen-Jun Li·Xue-Ying Li·Qian-Qian Chen·Ji-Ming Guo
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Abstract

The problem posed by Hoffman, namely, to characterize graphs whose second largest adjacency eigenvalue is at most \(1\), was first studied by D.~M.~Cvetković in 1982 [\textit{Publ. Inst. Math. (Beograd)} \textbf{31} (1982), 15--20]. In this paper, we completely characterize all connected planar graphs whose second largest eigenvalue does not exceed $1$.

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Zihao Geng, Zhiwen Wang, Wen-Jun Li, Xue-Ying Li, Qian-Qian Chen, Ji-Ming Guo. 2026-10-17. Planar graphs whose second largest eigenvalue does not exceed 1. https://arxiv.org/abs/2610.24716

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