{
  "abstract": "Let f be a labeling of the edges of a finite graph G by positive integers, and let the weight of a path be the sum of the labels of its edges. The labeling is a geodesic Leech labeling if the weights of the geodesics are exactly 1, 2, ..., t_gp(G), each occurring once, where t_gp(G) is the geodesic path number of G. Let W_n be the wheel on n vertices, a hub joined to an (n-1)-cycle. Our main result is an upper bound: if n >= 5 and W_n is geodesic Leech, then n <= 40. The proof quantifies, via a finite Fourier kernel, the Sidon-type structure of the spoke labels, in which only the cyclically adjacent pairs are allowed as defects, and closes the last three cases with a six-variable Parseval argument. In the other direction, explicit labelings of W_7, ..., W_13, found by a computer search, answer in the negative a problem of Lakshmanan S. and Manattu, who had found labelings of W_5 and W_6 and expected every W_n with n >= 7 to be a non-geodesic Leech graph. Writing E for the set of n >= 5 for which W_n is geodesic Leech, we obtain {5, 6, ..., 13} is contained in E, which is contained in {5, 6, ..., 40}.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.02544",
  "author_total": 1,
  "authors": [
    {
      "name": "Junyeop Yim"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/e5vacf0zzh8tp.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.02544",
  "fulltext_url": null,
  "id": "e5vacf0zzh8tp",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.02544",
  "language": null,
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.CO"
    ],
    [
      "arxiv",
      "math.NT"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2609.02544",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-02",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/e5vacf0zzh8tp.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:18:20Z",
      "native_id": "2609.02544",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.02544"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.NT",
      "subfield": "algebra-number-theory"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.CO",
      "subfield": "combinatorics"
    }
  ],
  "title": "A finiteness theorem for geodesic Leech wheels",
  "title_text": "A finiteness theorem for geodesic Leech wheels",
  "type": "preprint",
  "updated_at": "2026-10-30T12:18:20Z",
  "url": "https://research.draconitic.com/paper/e5vacf0zzh8tp",
  "venue": "arXiv",
  "versions": []
}