{
  "abstract": "Let $\\mathcal P_1$ denote the class of 1-planar graphs and let $tC_5$ be the disjoint union of $t$ copies of $C_5$. For every fixed $t\\ge3$ and all sufficiently large $n$, we determine the unique $n$-vertex $tC_5$-free graph in $\\mathcal P_1$ with maximum adjacency spectral radius, answering Problem 1 of Li, Wang and Zhao. The proof first gives a structural description of every extremizer. After two dominating vertices are removed, the remainder consists of copies of the seven-vertex graph $B=K_1\\vee2K_3$ together with at most one bounded connected core. This follows from a two-family covering theorem for 1-planar $K_2$-joins and the sharp packing--defect inequality \\[ 12v(Q)-7e(Q)\\ge1-10ν_5(Q). \\] The same inequality yields an exact edge-extremal result for remainders with bounded pentagon packing. A normalized resolvent then cancels the repeated $B$-components, and finite moment comparisons force all packing and all nonzero defect into one core and identify that core uniquely in each residue class modulo $7$. The case $t=3$ is the pentagon-free boundary case and is completed by one exact finite component lemma.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.08888",
  "author_total": 1,
  "authors": [
    {
      "name": "Zhanhe Zhang"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/akpfhhnz6werf.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.08888",
  "fulltext_url": null,
  "id": "akpfhhnz6werf",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.08888",
  "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": "W7220950450",
  "pdf_url": "https://arxiv.org/pdf/2610.08888",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-06",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/akpfhhnz6werf.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:27:42Z",
      "native_id": "2610.08888",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.08888"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CO",
      "subfield": "combinatorics"
    }
  ],
  "title": "Spectral Extremal 1-Planar Graphs with Bounded Pentagon Packing",
  "title_text": "Spectral Extremal 1-Planar Graphs with Bounded Pentagon Packing",
  "type": "preprint",
  "updated_at": "2026-10-30T12:27:42Z",
  "url": "https://research.draconitic.com/paper/akpfhhnz6werf",
  "venue": "arXiv",
  "versions": []
}