{
  "abstract": "The Wiener index $W(G)$ of a connected graph $G$ is the sum of the distances between all unordered pairs of vertices. A vertex $x$ is a Šoltés vertex if $G-x$ is connected and $W(G-x)=W(G)$. We construct an infinite family of graphs in which the proportion of Šoltés vertices is strictly greater than $(\\sqrt{21}-3)/3=0.5275\\ldots>1/2$ and decreases to this value from $2/3$. The family is also described by a generalized Pell equation and starts from a $12$-vertex example of Akhmejanova et al. (Discrete Appl. Math. 325 (2023) 37-42). We also show that the construction remains valid after adding edges among certain vertices.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2611.01808",
  "author_total": 1,
  "authors": [
    {
      "name": "A. A. Dobrynin"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/f6sn84kkm22e2.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2611.01808",
  "fulltext_url": null,
  "id": "f6sn84kkm22e2",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2611.01808",
  "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"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2611.01808",
  "pmcid": null,
  "pmid": null,
  "published": "2026-11-01",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/f6sn84kkm22e2.ris",
  "sources": [
    {
      "first_seen": "2026-11-03T12:21:10Z",
      "native_id": "2611.01808",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2611.01808"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CO",
      "subfield": "combinatorics"
    }
  ],
  "title": "An infinite family of graphs with Šoltés fraction uniformly above one half",
  "title_text": "An infinite family of graphs with Šoltés fraction uniformly above one half",
  "type": "preprint",
  "updated_at": "2026-11-05T15:20:22Z",
  "url": "https://research.draconitic.com/paper/f6sn84kkm22e2",
  "venue": "arXiv",
  "versions": []
}