{
  "abstract": "For any Galois field $\\mathbb{F}_q$ with $q$ elements and any positive integers $m$ and $n$, the directed graph $D(q;m,n)$ has vertex set $\\mathbb{F}_q\\times\\mathbb{F}_q$, and there is an arc from vertex $(x_1,x_2)$ to vertex $(y_1,y_2)$ if and only if $x_2+y_2=x_1^my_1^n$. It was conjectured in earlier work that two digraphs $D(q;m_1,n_1)$ and $D(q;m_2,n_2)$ are isomorphic if and only if there exists an integer $k$ relatively prime to $q-1$ such that $m_2\\equiv km_1$ and $n_2 \\equiv kn_1$, where both congruences are modulo $q-1$. We prove this conjecture over prime fields and construct an infinite family of counterexamples over extension fields.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.06735",
  "author_total": 3,
  "authors": [
    {
      "name": "Alexander M. Kodess"
    },
    {
      "name": "Felix Lazebnik"
    },
    {
      "name": "Mikhail Muzychuk"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/275wc9azbrz2v.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.06735",
  "fulltext_url": null,
  "id": "275wc9azbrz2v",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.06735",
  "language": null,
  "licence": "CC-BY-NC-ND-4.0",
  "licence_label": "CC BY-NC-ND 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by-nc-nd/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.CO"
    ],
    [
      "openalex",
      "2607|Finite Group Theory Research"
    ]
  ],
  "openalex": "W7220704739",
  "pdf_url": "https://arxiv.org/pdf/2610.06735",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-05",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/275wc9azbrz2v.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:27:10Z",
      "native_id": "2610.06735",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.06735"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CO",
      "subfield": "combinatorics"
    }
  ],
  "title": "Isomorphism Criterion of Monomial Digraphs over Prime Fields",
  "title_text": "Isomorphism Criterion of Monomial Digraphs over Prime Fields",
  "type": "preprint",
  "updated_at": "2026-10-30T12:27:10Z",
  "url": "https://research.draconitic.com/paper/275wc9azbrz2v",
  "venue": "arXiv",
  "versions": []
}