{
  "abstract": "We uniformly study directed Praeger--Xu graphs and Praeger's generalized family $\\overrightarrow{\\operatorname{PX}}(Γ,r,s)$, without requiring that $s\\mid r$ and $Γ$ is an undirected graph. Assuming that $Γ\\times\\overrightarrow{K}_2$ is connected, we determine the full automorphism group of $\\overrightarrow{\\operatorname{PX}}(Γ,r,s)$ for every $r$ and $s$, prove connectivity, characterize vertex-transitivity, and give an equivalent criterion for $t$-arc-transitivity. We also study when $\\overrightarrow{\\operatorname{PX}}(Γ,r,s)$ is a Cayley graph. We also give two applications. First, we give a new family of twin-free connected arc-transitive digraphs of valency $4$ whose vertex stabilizers have exponential growth. We also give a connected regular digraph that is not vertex-transitive but whose direct product with a directed cycle is Cayley.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.35623",
  "author_total": 2,
  "authors": [
    {
      "name": "Zhaochen Ding"
    },
    {
      "name": "Ci Xuan Wu"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/6tf07j5swv53g.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.35623",
  "fulltext_url": null,
  "id": "6tf07j5swv53g",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.35623",
  "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.GR"
    ],
    [
      "openalex",
      "2607|Finite Group Theory Research"
    ]
  ],
  "openalex": "W7223890983",
  "pdf_url": "https://arxiv.org/pdf/2610.35623",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-26",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/6tf07j5swv53g.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:35:40Z",
      "native_id": "2610.35623",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.35623"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.GR",
      "subfield": "algebra-number-theory"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.CO",
      "subfield": "combinatorics"
    }
  ],
  "title": "Generalizing Praeger--Xu graphs",
  "title_text": "Generalizing Praeger--Xu graphs",
  "type": "preprint",
  "updated_at": "2026-10-30T12:35:40Z",
  "url": "https://research.draconitic.com/paper/6tf07j5swv53g",
  "venue": "arXiv",
  "versions": []
}