{
  "abstract": "Let $G=\\Cay(\\mathbb{Z}_n,S)$ be a $3$-valent circulant digraph with connection set $S=\\{0,s,t\\}$, where $s,t\\in\\mathbb{Z}_n^*$ and $t\\neq\\pm s$. Determining the automorphism group of its endomorphism monoid reduces to determining the subgroup $U_S(\\mathbb{Z}_n)\\leq\\mathbb{Z}_n^*$ that normalizes $\\End(G)$. In this paper, we first establish necessary and sufficient conditions for a unit circulant digraph without $2$-cycles to admit an endomorphism whose image induces a directed cycle. Using this characterization, we explicitly determine $U_S(\\mathbb{Z}_n)$ for the previously unresolved $0$-unit $3$-valent family.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.12318",
  "author_total": 1,
  "authors": [
    {
      "name": "Chenhui Lv"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/02fythgwn9b3r.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.12318",
  "fulltext_url": null,
  "id": "02fythgwn9b3r",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.12318",
  "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"
    ],
    [
      "openalex",
      "2607|Finite Group Theory Research"
    ]
  ],
  "openalex": "W7212823474",
  "pdf_url": "https://arxiv.org/pdf/2609.12318",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-11",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/02fythgwn9b3r.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:21:11Z",
      "native_id": "2609.12318",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.12318"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CO",
      "subfield": "combinatorics"
    }
  ],
  "title": "Automorphism groups of endomorphism monoids of $0$-unit $3$-valent circulant digraphs",
  "title_text": "Automorphism groups of endomorphism monoids of $0$-unit $3$-valent circulant digraphs",
  "type": "preprint",
  "updated_at": "2026-10-30T12:21:11Z",
  "url": "https://research.draconitic.com/paper/02fythgwn9b3r",
  "venue": "arXiv",
  "versions": []
}