{
  "abstract": "Circulant digraphs form a prominent class of Cayley digraphs defined on finite cyclic groups. Building on the existing classification of $2$-arc-transitive circulant graphs, this paper presents a complete classification of $2$-distance-transitive circulant digraphs. Our main theorem establishes that every connected $2$-distance-transitive circulant digraph is isomorphic to one of the following: the undirected cycle $C_n$, the complete bipartite graph $\\K_{\\frac{n}{2},\\frac{n}{2}}$, the complete multipartite graph $\\K_{m[b]}$ with $m\\geq 3,b\\geq 2$, the graph $\\K_{\\frac{n}{2},\\frac{n}{2}}-\\frac{n}{2}\\K_2$ for odd $\\frac{n}{2}$, prime-order Paley graphs, the directed cycle $\\overrightarrow{C}_n$, the oriented graph \\(G(p^m,r)\\) satisfying Condition~\\ref{p-power-normal-2dt-cond}, the oriented graph \\( C_r(b,1)\\) with $r\\geq 3,b\\geq 2$ and $rb=n$, the lexicographic product oriented graph \\( G(p^m,r)[\\overline{\\K}_d]\\) where \\(G(p^m,r)\\) obeys Condition~\\ref{p-power-normal-2dt-cond}.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.19734",
  "author_total": 6,
  "authors": [
    {
      "name": "Wei Jin"
    },
    {
      "name": "Cai Xia Li"
    },
    {
      "name": "Ping Shan Li"
    },
    {
      "name": "Xiao Lin Sun"
    },
    {
      "name": "Jue Wu"
    },
    {
      "name": "Fan Yang"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/748qa5jbpry5g.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.19734",
  "fulltext_url": null,
  "id": "748qa5jbpry5g",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.19734",
  "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": "W7213585948",
  "pdf_url": "https://arxiv.org/pdf/2609.19734",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-17",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/748qa5jbpry5g.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:22:23Z",
      "native_id": "2609.19734",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.19734"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CO",
      "subfield": "combinatorics"
    }
  ],
  "title": "On 2-distance-transitive circulant digraphs",
  "title_text": "On 2-distance-transitive circulant digraphs",
  "type": "preprint",
  "updated_at": "2026-10-30T12:22:23Z",
  "url": "https://research.draconitic.com/paper/748qa5jbpry5g",
  "venue": "arXiv",
  "versions": []
}