{
  "abstract": "We determine the automorphism groups of direct products of finite connected twin-free bipartite graphs whose factors are different from $K_2$. The product is generally disconnected, so the problem requires both the automorphism groups of its components and a criterion for component isomorphism. We retain the order of the bipartition classes and use the fibre product over $K_2$. An edge-relation construction, together with McKenzie's strict refinement theorem, yields unique fibre-prime factorization and a coordinate description of every specified isomorphism. After refining the original factors, component isomorphism classes are described by intersections of factor-symmetry orbits with a set of admissible labels. The stabilizer of a label acts faithfully as the fullautomorphism group of its component. These data determine the full automorphism group, including products with repeated or fibre-composite factors. For products of fibre powers of one prime graph, we compute the component groups and express their multiplicities through a subset-sum polynomial. We also obtain an explicit semidirect product for a mixed product with one nonbipartite factor and explain its relation to known stability results. An application recovers the known double-cover groups of bipartite generalized Petersen graphs.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2611.00775",
  "author_total": 1,
  "authors": [
    {
      "name": "Xiaomeng Wang"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/cth89wxd3tnjw.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2611.00775",
  "fulltext_url": null,
  "id": "cth89wxd3tnjw",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2611.00775",
  "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/2611.00775",
  "pmcid": null,
  "pmid": null,
  "published": "2026-11-01",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/cth89wxd3tnjw.ris",
  "sources": [
    {
      "first_seen": "2026-11-03T12:21:10Z",
      "native_id": "2611.00775",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2611.00775"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CO",
      "subfield": "combinatorics"
    }
  ],
  "title": "Fibre factorization and automorphisms of direct products of bipartite graphs",
  "title_text": "Fibre factorization and automorphisms of direct products of bipartite graphs",
  "type": "preprint",
  "updated_at": "2026-11-05T15:20:22Z",
  "url": "https://research.draconitic.com/paper/cth89wxd3tnjw",
  "venue": "arXiv",
  "versions": []
}