{
  "abstract": "Let $G$ be a finite group. The co-intersection graph $Δ_G ^c$ of $G$ has as its vertices the nontrivial proper subgroups of $G$, with edges joining those pairs of subgroups which intersect trivially. It is clear that every connected component of $Δ_G ^c$ has diameter at most three. In this Note, we show that when $T$ is a nonabelian finite simple group, $Δ_T$ is connected of diameter exactly two. We also make several observations about the extent to which a finite group is determined by its co-intersection graph, and about the class of finite graphs arising as co-intersection graphs.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.07948",
  "author_total": 2,
  "authors": [
    {
      "name": "Henry Bradford"
    },
    {
      "name": "Kamilla Rekvényi"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/251spmnmghr0x.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.07948",
  "fulltext_url": null,
  "id": "251spmnmghr0x",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.07948",
  "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.GR"
    ],
    [
      "openalex",
      "2607|Finite Group Theory Research"
    ]
  ],
  "openalex": "W7212003970",
  "pdf_url": "https://arxiv.org/pdf/2609.07948",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-07",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/251spmnmghr0x.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:19:58Z",
      "native_id": "2609.07948",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.07948"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.GR",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "Co-intersection graphs of nonabelian finite simple groups have diameter two",
  "title_text": "Co-intersection graphs of nonabelian finite simple groups have diameter two",
  "type": "preprint",
  "updated_at": "2026-10-30T12:19:58Z",
  "url": "https://research.draconitic.com/paper/251spmnmghr0x",
  "venue": "arXiv",
  "versions": []
}