{
  "abstract": "We study graphs admitting a strictly matched involution, i.e., graphs for which a strictly matched involution exists. A strictly matched involution of a graph $G$ is a self-inverse graph automorphism $f$ with the properties that the fixed point set of $f$ induces a complete subgraph in $G$ and, for the vertices that are no fixed points, every vertex is connected to its image under $f$ by an edge. Andres, Huggan, Mc Inerney, and Nowakowski (2019) determined upper and lower bounds for the number $A(n)$ of graphs admitting a strictly matched involution on $n$ vertices. We improve the upper bound and we compute the exact values for the number $A(n)$ for all $n\\leq11$. Furthermore, we use combinatorial enumeration techniques and a decomposition lemma to determine the number $C(n,m)$ of graphs admitting a strictly matched involution with $n$ vertices and $m$ edges for several infinite classes of pairs $(n,m)$.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2611.06703",
  "author_total": 2,
  "authors": [
    {
      "name": "Stephan Dominique Andres"
    },
    {
      "name": "Igor Režan"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/1ymehwbmkbcnb.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2611.06703",
  "fulltext_url": null,
  "id": "1ymehwbmkbcnb",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2611.06703",
  "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/2611.06703",
  "pmcid": null,
  "pmid": null,
  "published": "2026-11-04",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/1ymehwbmkbcnb.ris",
  "sources": [
    {
      "first_seen": "2026-11-05T15:21:00Z",
      "native_id": "2611.06703",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2611.06703"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CO",
      "subfield": "combinatorics"
    }
  ],
  "title": "Counting graphs admitting a strictly matched involution",
  "title_text": "Counting graphs admitting a strictly matched involution",
  "type": "preprint",
  "updated_at": "2026-11-09T00:20:30Z",
  "url": "https://research.draconitic.com/paper/1ymehwbmkbcnb",
  "venue": "arXiv",
  "versions": []
}