{
  "abstract": "For integers $n\\ge3$ and $2\\leΔ\\le n-1$, let $λ_1(n,Δ)$ be the maximum adjacency spectral radius among all connected nonregular graphs of order $n$ and maximum degree $Δ$. Liu conjectured that for each fixed integer $Δ\\ge3$, \\[ \\lim_{n\\to\\infty}n^2\\bigl(Δ-λ_1(n,Δ)\\bigr)= \\begin{cases} (Δ-1)π^2/4,&\\text{if $Δ$ is odd};\\\\ (Δ-2)π^2/2,&\\text{if $Δ$ is even}. \\end{cases} \\] He proved the case $Δ=3$ and $Δ=4$. We prove the conjecture when $Δ\\ge5$ is odd.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.26044",
  "author_total": 2,
  "authors": [
    {
      "name": "Zejun Huang"
    },
    {
      "name": "Chenxi Yang"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/ers1027pc71yt.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.26044",
  "fulltext_url": null,
  "id": "ers1027pc71yt",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.26044",
  "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": "W7214087558",
  "pdf_url": "https://arxiv.org/pdf/2609.26044",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-22",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/ers1027pc71yt.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:23:43Z",
      "native_id": "2609.26044",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.26044"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CO",
      "subfield": "combinatorics"
    }
  ],
  "title": "Extremal spectral radius of nonregular graphs with a fixed odd maximum degree",
  "title_text": "Extremal spectral radius of nonregular graphs with a fixed odd maximum degree",
  "type": "preprint",
  "updated_at": "2026-10-30T12:23:43Z",
  "url": "https://research.draconitic.com/paper/ers1027pc71yt",
  "venue": "arXiv",
  "versions": []
}