{
  "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 $1$.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.24716",
  "author_total": 6,
  "authors": [
    {
      "name": "Zihao Geng"
    },
    {
      "name": "Zhiwen Wang"
    },
    {
      "name": "Wen-Jun Li"
    },
    {
      "name": "Xue-Ying Li"
    },
    {
      "name": "Qian-Qian Chen"
    },
    {
      "name": "Ji-Ming Guo"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/277wbr00y5xvt.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.24716",
  "fulltext_url": null,
  "id": "277wbr00y5xvt",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.24716",
  "language": null,
  "licence": "LicenseRef-arXiv-nonexclusive-1.0",
  "licence_label": "arXiv licence",
  "licence_source": "article",
  "licence_url": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.CO"
    ],
    [
      "openalex",
      "2608|Graph theory and applications"
    ]
  ],
  "openalex": "W7223029128",
  "pdf_url": "https://arxiv.org/pdf/2610.24716",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-17",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/277wbr00y5xvt.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:30:57Z",
      "native_id": "2610.24716",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.24716"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CO",
      "subfield": "combinatorics"
    }
  ],
  "title": "Planar graphs whose second largest eigenvalue does not exceed 1",
  "title_text": "Planar graphs whose second largest eigenvalue does not exceed 1",
  "type": "preprint",
  "updated_at": "2026-10-30T12:33:44Z",
  "url": "https://research.draconitic.com/paper/277wbr00y5xvt",
  "venue": "arXiv",
  "versions": []
}