{
  "abstract": "We prove that if $φ$ is an isomorphism between two connected Cayley graphs of abelian groups, and $φ$ respects the natural edge-colourings of the Cayley graphs, then $φ$ is the composition of a group isomorphism and a colour-preserving graph automorphism. This implies that if every colour-preserving automorphism of a connected abelian Cayley graph $Cay(G;S)$ is an affine map, then the same is true for every colour-permuting automorphism. We also show that this property holds if and only if the subgroup generated by $\\{\\, s \\in S \\mid 2s \\neq c \\,\\} \\cup \\{c\\}$ has index $\\le 2$ for every element $c$ of order $2$ in $G$.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.09563",
  "author_total": 2,
  "authors": [
    {
      "name": "Shirin Alimirzaei"
    },
    {
      "name": "Dave Witte Morris"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/6fb59zhvx2d7g.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.09563",
  "fulltext_url": null,
  "id": "6fb59zhvx2d7g",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.09563",
  "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": "W7212151355",
  "pdf_url": "https://arxiv.org/pdf/2609.09563",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-09",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/6fb59zhvx2d7g.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:20:15Z",
      "native_id": "2609.09563",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.09563"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CO",
      "subfield": "combinatorics"
    }
  ],
  "title": "Isomorphisms of abelian Cayley graphs with their natural edge-colouring",
  "title_text": "Isomorphisms of abelian Cayley graphs with their natural edge-colouring",
  "type": "preprint",
  "updated_at": "2026-10-30T12:20:15Z",
  "url": "https://research.draconitic.com/paper/6fb59zhvx2d7g",
  "venue": "arXiv",
  "versions": []
}