{
  "abstract": "An outerplanar graph is \\emph{maximal} if no edge can be added without losing outerplanarity. Lin and Ning determined the outerplanar graph with the largest spectral radius, and the maximizer is a maximal outerplanar graph. We determine the minimizer. In this paper, we prove that every $n$-vertex maximal outerplanar graph $G$ satisfies $ρ(G)\\geρ(F_n)$, where $F_n$ is the zig-zag triangulation of the $n$-gon, that is, the square of the path on $n$ vertices, with equality if and only if $G=F_n$. The proof uses three local operations on maximal outerplanar graphs, each of which strictly decreases the spectral radius: the first reverses the way a piece is attached along a chord, and the second and third move a piece from one vertex to its twin across a chord when the twin carries nothing or a single ear, respectively. A graph at which no operation applies is $F_n$, or has spectral radius greater than $4$, or consists of a central triangle with three zig-zag blades of at least three triangles each and has at most $15$ vertices; in the last case it contains one of two explicit graphs on $12$ vertices whose spectral radius exceeds that of $F_{15}$. Since $ρ(F_n)<4$ for all $n$, this completes the proof. The numerical inequalities used along the way are certified by explicit integer vectors with small entries.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.33333",
  "author_total": 1,
  "authors": [
    {
      "name": "Suil O"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/04964db51fda1.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.33333",
  "fulltext_url": null,
  "id": "04964db51fda1",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.33333",
  "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": "W7214769987",
  "pdf_url": "https://arxiv.org/pdf/2609.33333",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-27",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/04964db51fda1.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:25:17Z",
      "native_id": "2609.33333",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.33333"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CO",
      "subfield": "combinatorics"
    }
  ],
  "title": "The minimum spectral radius of maximal outerplanar graphs",
  "title_text": "The minimum spectral radius of maximal outerplanar graphs",
  "type": "preprint",
  "updated_at": "2026-10-30T12:25:17Z",
  "url": "https://research.draconitic.com/paper/04964db51fda1",
  "venue": "arXiv",
  "versions": []
}