{
  "abstract": "In this paper, we study perfect codes in bi-Cayley graphs, focusing on when two subgroups $H$ and $K$ of a group G can form a perfect code of the form $H_0 \\cup K_1$. We first consider the problem for a general group G and then examine what happens for special classes of groups, particularly abelian groups. Along the way, we obtain several results, including a necessary and sufficient condition for normal subgroups to form a perfect code, as well as an equivalent condition for abelian groups in terms of their Sylow 2-subgroups. Finally, we study the same problem for dihedral groups, providing results for this important class of non-abelian groups.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.16235",
  "author_total": 3,
  "authors": [
    {
      "name": "Masoumeh Koohestani"
    },
    {
      "name": "Nasrin Soltankhah"
    },
    {
      "name": "Mohsen Ghasemi"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/9qnv7ga84zzh7.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.16235",
  "fulltext_url": null,
  "id": "9qnv7ga84zzh7",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.16235",
  "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",
      "2607|Finite Group Theory Research"
    ]
  ],
  "openalex": "W7221763039",
  "pdf_url": "https://arxiv.org/pdf/2610.16235",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-12",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/9qnv7ga84zzh7.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:29:15Z",
      "native_id": "2610.16235",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.16235"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CO",
      "subfield": "combinatorics"
    }
  ],
  "title": "Subgroup Perfect Codes in Bi-Cayley Graphs",
  "title_text": "Subgroup Perfect Codes in Bi-Cayley Graphs",
  "type": "preprint",
  "updated_at": "2026-10-30T12:29:15Z",
  "url": "https://research.draconitic.com/paper/9qnv7ga84zzh7",
  "venue": "arXiv",
  "versions": []
}