{
  "abstract": "We construct an infinite family of directed strongly regular graphs (DSRGs) with intransitive full automorphism groups whose Weisfeiler--Leman closure are association schemes of rank 6. This is the smallest possible rank for an association scheme admitting a proper DSRG merging. We also exhibit rigid sporadic DSRGs with the same closure property, showing that combinatorial regularity, group-theoretic symmetry, and Weisfeiler--Leman regularity capture fundamentally different aspects of graph structure.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.25282",
  "author_total": 1,
  "authors": [
    {
      "name": "Štefan Gyürki"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/6y8yh7y43x626.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.25282",
  "fulltext_url": null,
  "id": "6y8yh7y43x626",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.25282",
  "language": null,
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.CO"
    ],
    [
      "openalex",
      "2607|Finite Group Theory Research"
    ]
  ],
  "openalex": "W7214086272",
  "pdf_url": "https://arxiv.org/pdf/2609.25282",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-21",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/6y8yh7y43x626.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:23:43Z",
      "native_id": "2609.25282",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.25282"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CO",
      "subfield": "combinatorics"
    }
  ],
  "title": "An infinite family of intransitive directed strongly regular graphs with rank 6 Weisfeiler--Leman closure",
  "title_text": "An infinite family of intransitive directed strongly regular graphs with rank 6 Weisfeiler--Leman closure",
  "type": "preprint",
  "updated_at": "2026-10-30T12:23:43Z",
  "url": "https://research.draconitic.com/paper/6y8yh7y43x626",
  "venue": "arXiv",
  "versions": []
}