{
  "abstract": "We study torsional rigidity on finite compact connected metric graphs with real \\(δ\\)-vertex strengths in the regime of strictly positive torsion. For a fixed total length \\(L>0\\), let \\(I_+\\) be the sum of the positive strengths and \\(I_-\\) the sum of the magnitudes of the negative strengths, with \\(I_+>I_-\\). We determine the sharp infimum and the exact threshold for a finite universal supremum. The supremum is finite precisely when \\(I_-<I_+/(1+LI_+)\\). In this regime, an interval with strengths \\(I_+\\) and \\(-I_-\\) at opposite endpoints attains the sharp Saint--Venant bound. At and beyond the threshold, torsional rigidity is unbounded even among three-vertex paths with the same data and strictly positive torsion. The sharp infimum is \\(L^2/(I_+-I_-)\\) throughout the range \\(I_+>I_-\\ge0\\). It is not attained by any finite graph and is approached by graphs with two vertices joined by increasingly many parallel edges of equal length, preserving both strength totals separately. A vertex-matrix formulation and explicit path examples clarify the relation between strength placement, spectral positivity, and solvability.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.38330",
  "author_total": 1,
  "authors": [
    {
      "name": "Sedef Özcan"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/dfggvka79b3d2.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.38330",
  "fulltext_url": null,
  "id": "dfggvka79b3d2",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.38330",
  "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.AP"
    ],
    [
      "arxiv",
      "math.CO"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2610.38330",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-28",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/dfggvka79b3d2.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:36:32Z",
      "native_id": "2610.38330",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.38330"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AP",
      "subfield": "analysis-pdes"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.CO",
      "subfield": "combinatorics"
    }
  ],
  "title": "Sharp Bounds on Torsional Rigidity of Metric Graphs with Signed Delta-Vertex Strengths",
  "title_text": "Sharp Bounds on Torsional Rigidity of Metric Graphs with Signed Delta-Vertex Strengths",
  "type": "preprint",
  "updated_at": "2026-11-01T12:20:50Z",
  "url": "https://research.draconitic.com/paper/dfggvka79b3d2",
  "venue": "arXiv",
  "versions": []
}