{
  "abstract": "A graph is edge-transitive if its automorphism group acts transitively on its edge set. This paper is devoted to a systematic study of cubic edge-transitive graphs of order $\\ell p^2$, where $p$ is a prime and $\\ell$ is an even integer. We first show that either $Γ$ is the unique cubic edge-transitive graph of order $18$, or its full automorphism group $\\mathrm{Aut}(Γ)$ contains a normal Sylow $p$-subgroup $P$ which is isomorphic to either $Z_{p^2}$ or $Z_{p}^2$. For the case $P\\cong Z_{p^2}$, we prove that $Γ$ is either arc-regular or edge-regular, and provide a complete classification of such graphs. For the case $P\\cong Z_{p}^2$, we prove that $Γ$ is a normal cover of certain known graphs. This work generalizes previous classifications by Zhou and Feng (2024), Lu et al.~(2004), and others. As an application, we obtain a classification of cubic edge-transitive graphs of order $\\ell p^2$ in the case where $\\ell$ is square-free.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.32351",
  "author_total": 3,
  "authors": [
    {
      "name": "Xue Wang"
    },
    {
      "name": "Jun-Jie Huang"
    },
    {
      "name": "Da-Wei Yang"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/cxj54gfk739gb.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.32351",
  "fulltext_url": null,
  "id": "cxj54gfk739gb",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.32351",
  "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": "W7223702939",
  "pdf_url": "https://arxiv.org/pdf/2610.32351",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-23",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/cxj54gfk739gb.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:35:19Z",
      "native_id": "2610.32351",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.32351"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.GR",
      "subfield": "algebra-number-theory"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.CO",
      "subfield": "combinatorics"
    }
  ],
  "title": "Cubic edge-transitive graphs of order $\\ell p^2$",
  "title_text": "Cubic edge-transitive graphs of order ℓ p^2",
  "type": "preprint",
  "updated_at": "2026-10-30T12:35:19Z",
  "url": "https://research.draconitic.com/paper/cxj54gfk739gb",
  "venue": "arXiv",
  "versions": []
}