{
  "abstract": "This note addresses Theorem 12 in the seminal paper ``$F$-degrees in graphs'' by G. Chartrand et al. (1987), which asserts the existence of $K_n$-irregular graphs for each $n \\ge 3$. Although this result is widely cited in the literature as an established fact, the original text lacks a complete proof. We show that for $n = 5$ and all $n \\ge 7$, the constructions as presented are not $K_n$-irregular, presumably due to typographical errors. Consequently, referencing this foundational work as containing a rigorous proof for the general case is not entirely accurate.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.30355",
  "author_total": 1,
  "authors": [
    {
      "name": "Tatiana Dovzhenok"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/9zkkfm100fc4j.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.30355",
  "fulltext_url": null,
  "id": "9zkkfm100fc4j",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.30355",
  "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",
      "1703|Advanced Graph Theory Research"
    ]
  ],
  "openalex": "W7214628319",
  "pdf_url": "https://arxiv.org/pdf/2609.30355",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-24",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/9zkkfm100fc4j.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:24:57Z",
      "native_id": "2609.30355",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.30355"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CO",
      "subfield": "combinatorics"
    }
  ],
  "title": "A short note on $K_{n}$-irregular graphs",
  "title_text": "A short note on K_n-irregular graphs",
  "type": "preprint",
  "updated_at": "2026-10-30T12:24:57Z",
  "url": "https://research.draconitic.com/paper/9zkkfm100fc4j",
  "venue": "arXiv",
  "versions": []
}