{
  "abstract": "We exhibit the joint symmetric distribution of the following two parameters on the set of unlabeled simple connected graphs with $n$ vertices. The first parameter is the maximal number of leaves attached to a vertex. The second parameter is the size of the largest set of vertices sharing the same closed neighborhood minus $1$. Apparently, this is the first example of a natural non-trivial equidistribution of graph parameters on unlabeled simple connected graphs with a fixed set of vertices. Our proof is enumerative, using the theory of species. Exhibiting an explicit bijection interchanging the two parameters remains an open problem.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": null,
  "author_total": 3,
  "authors": [
    {
      "name": "Florian Fürnsinn"
    },
    {
      "name": "Moritz Gangl"
    },
    {
      "name": "Martin Rubey"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/0ay1zhz7nyfgc.bib",
  "cited_by": 0,
  "doi": "10.37236/15312",
  "fulltext_url": null,
  "id": "0ay1zhz7nyfgc",
  "issns": [
    "1077-8926"
  ],
  "landing_url": "https://www.combinatorics.org/ojs/index.php/eljc/article/view/v33i4p32",
  "language": null,
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "journal",
  "licence_url": "https://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": null,
  "native_subjects": [],
  "openalex": null,
  "pdf_url": "https://www.combinatorics.org/ojs/index.php/eljc/article/download/v33i4p32/pdf",
  "pmcid": null,
  "pmid": null,
  "published": "2026-11-06",
  "publisher": "The Electronic Journal of Combinatorics",
  "ris": "https://research.draconitic.com/paper/0ay1zhz7nyfgc.ris",
  "sources": [
    {
      "first_seen": "2026-11-06T12:20:56Z",
      "native_id": "10.37236/15312",
      "source": "crossref",
      "url": "https://www.combinatorics.org/ojs/index.php/eljc/article/view/v33i4p32"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "issn:1077-8926",
      "subfield": "combinatorics"
    }
  ],
  "title": "Unexpectedly, a Symmetry on Unlabeled Graphs",
  "title_text": "Unexpectedly, a Symmetry on Unlabeled Graphs",
  "type": "peer-reviewed",
  "updated_at": "2026-11-08T00:21:33Z",
  "url": "https://research.draconitic.com/paper/0ay1zhz7nyfgc",
  "venue": "The Electronic Journal of Combinatorics",
  "versions": []
}