{
  "abstract": "A graph $G$ is $F$-free if it does not contain $F$ as a subgraph. Let $\\mathrm{spex}(n,F)$ be the maximum spectral radius over all $n$-vertex $F$-free outerplanar graphs. For integers $t\\geq1$ and $l\\geq2$, let $P_{t\\cdot l}$ be the starlike tree with $t$ branches of length $l-1$. For sufficiently large $n$, Yin, Li, and Meng [arXiv:2504.04364v1] characterized the unique extremal graph for $\\mathrm{spex}(n,P_{t\\cdot l})$ when $t=1$, $t=2$, or $t\\geq4$. They left the case $t=3$ open and proposed a natural candidate for the extremal graph. We show that this candidate is not extremal and determine the unique extremal graph for $\\mathrm{spex}(n,P_{3\\cdot l})$. For every $l\\geq3$ and all sufficiently large $n$, this unique extremal graph is $K_1\\vee\\bigl(2P_{2l-3}\\cup qP_{l-2}\\cup P_r\\bigr),$ where $q$ and $r$ are integers satisfying $n=2(2l-3)+q(l-2)+r+1,$ $q\\geq0,$ $0\\leq r<l-2.$",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.24080",
  "author_total": 3,
  "authors": [
    {
      "name": "Fulong Ye"
    },
    {
      "name": "Yuxiang Liu"
    },
    {
      "name": "Ligong Wang"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/2cn90xabkh65f.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.24080",
  "fulltext_url": null,
  "id": "2cn90xabkh65f",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.24080",
  "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": "W7214049336",
  "pdf_url": "https://arxiv.org/pdf/2609.24080",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-21",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/2cn90xabkh65f.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:23:27Z",
      "native_id": "2609.24080",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.24080"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CO",
      "subfield": "combinatorics"
    }
  ],
  "title": "Extremal spectral result of outerplanar graphs without $P_{3\\cdot l}$",
  "title_text": "Extremal spectral result of outerplanar graphs without P_3· l",
  "type": "preprint",
  "updated_at": "2026-10-30T12:23:27Z",
  "url": "https://research.draconitic.com/paper/2cn90xabkh65f",
  "venue": "arXiv",
  "versions": []
}