{
  "abstract": "We study inverse-closed generator additions of minimum size that make the optimal pebbling number of a finite Cayley graph at most three while preserving its specified regular action. A weighted vertex-cover formulation on inverse orbits yields an $O(|Γ|^2)$ algorithm for abelian groups in the explicit multiplication-table model. We derive formulas for central involutions and cubelike graphs, with an inverse-closure correction determined by square roots in the uncovered set. The exact thresholds are $2^{d-1}-d$ for hypercubes ($d\\ge1$), and $3$ for standard Keller graphs when $d=2$ and $2^{d-1}$ when $d\\ge3$. Every admissible augmentation of either family has ordinary pebbling number equal to its order.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.41306",
  "author_total": 3,
  "authors": [
    {
      "name": "Yuan Yang"
    },
    {
      "name": "Bocheng Li"
    },
    {
      "name": "Qingzhong Ji"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/afj1rtxz00ty8.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.41306",
  "fulltext_url": null,
  "id": "afj1rtxz00ty8",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.41306",
  "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": null,
  "pdf_url": "https://arxiv.org/pdf/2610.41306",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-30",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/afj1rtxz00ty8.ris",
  "sources": [
    {
      "first_seen": "2026-11-02T12:21:20Z",
      "native_id": "2610.41306",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.41306"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CO",
      "subfield": "combinatorics"
    }
  ],
  "title": "Pebbling Numbers and Generator Reinforcement of Cayley Graphs",
  "title_text": "Pebbling Numbers and Generator Reinforcement of Cayley Graphs",
  "type": "preprint",
  "updated_at": "2026-11-04T15:20:52Z",
  "url": "https://research.draconitic.com/paper/afj1rtxz00ty8",
  "venue": "arXiv",
  "versions": []
}