{
  "abstract": "We construct an infinite family of Neumaier graphs of coherent rank five, answering the existence question at the smallest possible coherent rank beyond the strongly regular case. For every prime power $q\\geqslant7$ with $q\\equiv3\\pmod4$, set $n=q+1$. Each graph in our construction has precisely five distinct eigenvalues, Neumaier parameters \\[ \\left( n(n-1)(n-3), \\frac{n^2(n-3)}2, \\frac{n(n^2-n-8)}4; \\frac{(n-2)^2}{2}, (n-1)(n-3) \\right), \\] and its adjacency matrix lies in the Bose--Mesner algebra of the four-class association scheme of Holzmann, Kharaghani, and Suda. Paley Hadamard matrices and Desarguesian mutually orthogonal Latin squares yield an infinite family whose smallest member has parameters $(280,160,96;18,35)$.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.02218",
  "author_total": 2,
  "authors": [
    {
      "name": "Gary Greaves"
    },
    {
      "name": "Zhao Kuang Tan"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/81n2v0n375mat.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.02218",
  "fulltext_url": null,
  "id": "81n2v0n375mat",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.02218",
  "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": "W7207691113",
  "pdf_url": "https://arxiv.org/pdf/2609.02218",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-02",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/81n2v0n375mat.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:18:20Z",
      "native_id": "2609.02218",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.02218"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CO",
      "subfield": "combinatorics"
    }
  ],
  "title": "Neumaier graphs of coherent rank five",
  "title_text": "Neumaier graphs of coherent rank five",
  "type": "preprint",
  "updated_at": "2026-10-30T12:18:20Z",
  "url": "https://research.draconitic.com/paper/81n2v0n375mat",
  "venue": "arXiv",
  "versions": []
}