{
  "abstract": "We define a quantum graph to be vertex-transitive if the join of its automorphism group is the maximum quantum relation on its quantum vertex set, in direct analogy with the classical case. All simple quantum graphs in $M_2(\\mathbb C)$ are vertex-transitive, but many simple quantum graphs in $M_3(\\mathbb C)$ are not vertex-transitive. We provide a complete classification of vertex-transitive quantum graphs in $M_3(\\mathbb C)$ up to isomorphism. To do this, we introduce a polynomial invariant for quantum graphs in $M_n(\\mathbb C)$, which we call the panoramic polynomial.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2605.30730",
  "author_total": 4,
  "authors": [
    {
      "name": "Mac Hayes"
    },
    {
      "name": "Trevor Jess"
    },
    {
      "name": "Andre Kornell"
    },
    {
      "name": "Remi Salinas Schmeis"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/d57h2vs9qpdpg.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2605.30730",
  "fulltext_url": null,
  "id": "d57h2vs9qpdpg",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2605.30730",
  "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.CO"
    ],
    [
      "arxiv",
      "math.OA"
    ],
    [
      "arxiv",
      "math.QA"
    ],
    [
      "arxiv",
      "quant-ph"
    ],
    [
      "openalex",
      "2610|Advanced Operator Algebra Research"
    ]
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  "openalex": "W7163004135",
  "pdf_url": "https://arxiv.org/pdf/2605.30730",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-24",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/d57h2vs9qpdpg.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:24:52Z",
      "native_id": "2605.30730",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2605.30730"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.QA",
      "subfield": "algebra-number-theory"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.OA",
      "subfield": "analysis-pdes"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.CO",
      "subfield": "combinatorics"
    },
    {
      "field": "physics",
      "origin": "arxiv:quant-ph",
      "subfield": "quantum"
    }
  ],
  "title": "Vertex-transitive quantum graphs",
  "title_text": "Vertex-transitive quantum graphs",
  "type": "preprint",
  "updated_at": "2026-10-30T12:24:57Z",
  "url": "https://research.draconitic.com/paper/d57h2vs9qpdpg",
  "venue": "arXiv",
  "versions": []
}