{
  "abstract": "Let $λ_1(n,Δ)$ be the maximum adjacency spectral radius among connected nonregular simple graphs of order $n$ and maximum degree $Δ$. Using effective resistance bounds, explicit comparison graphs and a one-dimensional Wirtinger inequality, we prove that, for every fixed integer $Δ\\ge3$, $λ_1(n,Δ)=Δ-c_Δπ^2/(4n^2)+O_Δ(n^{-5/2})$ as $n\\to\\infty$, where $c_Δ=Δ-1$ for odd $Δ$ and $c_Δ=2(Δ-2)$ for even $Δ$. This proves the asymptotic conjecture posed by Liu [J. Combin. Theory Ser. B 169 (2024), Conjecture 7.1].",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.04947",
  "author_total": 2,
  "authors": [
    {
      "name": "Hangxi Cha"
    },
    {
      "name": "Haiying Shan"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/3tzdaedt61my5.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.04947",
  "fulltext_url": null,
  "id": "3tzdaedt61my5",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.04947",
  "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": "W7220743464",
  "pdf_url": "https://arxiv.org/pdf/2610.04947",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-14",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/3tzdaedt61my5.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:29:35Z",
      "native_id": "2610.04947",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.04947"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CO",
      "subfield": "combinatorics"
    }
  ],
  "title": "Asymptotic maximum spectral radius of nonregular graphs",
  "title_text": "Asymptotic maximum spectral radius of nonregular graphs",
  "type": "preprint",
  "updated_at": "2026-10-30T12:29:35Z",
  "url": "https://research.draconitic.com/paper/3tzdaedt61my5",
  "venue": "arXiv",
  "versions": []
}