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PreprintarXiv licencearXiv

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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Cite

BibTeXRIS
BibTeX
@misc{geng2026planar,
  title = {{Planar graphs whose second largest eigenvalue does not exceed 1}},
  author = {Zihao Geng and Zhiwen Wang and Wen-Jun Li and Xue-Ying Li and Qian-Qian Chen and Ji-Ming Guo},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.24716},
  eprint = {2610.24716},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.24716},
}
RIS
TY  - UNPB
TI  - Planar graphs whose second largest eigenvalue does not exceed 1
AU  - Zihao Geng
AU  - Zhiwen Wang
AU  - Wen-Jun Li
AU  - Xue-Ying Li
AU  - Qian-Qian Chen
AU  - Ji-Ming Guo
PY  - 2026
DA  - 2026/10/17
PB  - arXiv
DO  - 10.48550/arxiv.2610.24716
UR  - https://arxiv.org/abs/2610.24716
AB  - 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 $1$.
ER  -