{
  "abstract": "The commuting graph of a noncommutative ring has its noncentral elements as vertices, with two distinct vertices adjacent when they commute. Akbari, Ghandehari, Hadian and Mohammadian conjectured that a full matrix ring over a finite field is determined, among rings with identity, by its commuting graph. In this paper, we prove the conjecture for every even matrix size.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.37150",
  "author_total": 2,
  "authors": [
    {
      "name": "Hamid Shahverdi"
    },
    {
      "name": "Vahid Shahverdi"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/fp0602x1a3atv.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.37150",
  "fulltext_url": null,
  "id": "fp0602x1a3atv",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.37150",
  "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.RA"
    ],
    [
      "openalex",
      "2602|Rings, Modules, and Algebras"
    ]
  ],
  "openalex": "W7224103960",
  "pdf_url": "https://arxiv.org/pdf/2610.37150",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-27",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/fp0602x1a3atv.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:35:53Z",
      "native_id": "2610.37150",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.37150"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.RA",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "Finite Matrix Rings of Even Size Are Determined by Their Commuting Graphs",
  "title_text": "Finite Matrix Rings of Even Size Are Determined by Their Commuting Graphs",
  "type": "preprint",
  "updated_at": "2026-10-30T12:35:53Z",
  "url": "https://research.draconitic.com/paper/fp0602x1a3atv",
  "venue": "arXiv",
  "versions": []
}