{
  "abstract": "This paper introduces a class of non-homogeneous self-similar constructions, called $ω$-substitution graph system, in which the interface vertices are determined by an infinite sequence $ω.$ The associated graph sequences naturally form compact metric measure spaces, and under suitable assumptions on $ω$, we establish their convergence in the Gromov-Hausdorff-Prokhorov sense. We determine the Hausdorff and box-counting dimensions of the limiting space. We further prove that the discrete Hausdorff dimension of the graph sequence coincides with the Hausdorff dimension of its scaling limit. As a direct application of the scaling limit, asymptotic formulas are derived for a class of generalized Wiener indices, which include the classical Wiener index and Kirchhoff index as special cases. Finally, closed-form expressions for these indices are also obtained.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2611.05960",
  "author_total": 3,
  "authors": [
    {
      "name": "Qingcheng Zeng"
    },
    {
      "name": "Yumei Xue"
    },
    {
      "name": "Cheng Zeng"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/eyqsjbg8v2rhj.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2611.05960",
  "fulltext_url": null,
  "id": "eyqsjbg8v2rhj",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2611.05960",
  "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.MG"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2611.05960",
  "pmcid": null,
  "pmid": null,
  "published": "2026-11-04",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/eyqsjbg8v2rhj.ris",
  "sources": [
    {
      "first_seen": "2026-11-05T15:21:00Z",
      "native_id": "2611.05960",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2611.05960"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.MG",
      "subfield": "geometry-topology"
    }
  ],
  "title": "Scaling Limits and Fractal Dimensions of $ω$-Substitution Graph Systems",
  "title_text": "Scaling Limits and Fractal Dimensions of ω-Substitution Graph Systems",
  "type": "preprint",
  "updated_at": "2026-11-09T00:20:30Z",
  "url": "https://research.draconitic.com/paper/eyqsjbg8v2rhj",
  "venue": "arXiv",
  "versions": []
}