{
  "abstract": "In this paper, we prove that every connected sesqui-regular graph with parameters $(n,k,c)$, where $c\\geq3$, and with smallest eigenvalue in $[-3,-2)$ is $1$-integrable if its valency is sufficiently large. The bound on $c$ is optimal: for every integer $t\\geq2$, the Cartesian product of the Shrikhande graph and $K_t$ is a connected sesqui-regular graph with parameters $(16t,t+5,2)$ and smallest eigenvalue $-3$, but it is not $1$-integrable.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.27700",
  "author_total": 2,
  "authors": [
    {
      "name": "Qianqian Yang"
    },
    {
      "name": "Ruo-Lan Ding"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/2vmqhcx7e97d5.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.27700",
  "fulltext_url": null,
  "id": "2vmqhcx7e97d5",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.27700",
  "language": null,
  "licence": "CC-BY-NC-ND-4.0",
  "licence_label": "CC BY-NC-ND 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by-nc-nd/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.CO"
    ],
    [
      "openalex",
      "2608|Graph theory and applications"
    ]
  ],
  "openalex": "W7214182459",
  "pdf_url": "https://arxiv.org/pdf/2609.27700",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-23",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/2vmqhcx7e97d5.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:24:00Z",
      "native_id": "2609.27700",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.27700"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CO",
      "subfield": "combinatorics"
    }
  ],
  "title": "The integrability of sesqui-regular graphs with smallest eigenvalue at least $-3$",
  "title_text": "The integrability of sesqui-regular graphs with smallest eigenvalue at least −3",
  "type": "preprint",
  "updated_at": "2026-10-30T12:24:00Z",
  "url": "https://research.draconitic.com/paper/2vmqhcx7e97d5",
  "venue": "arXiv",
  "versions": []
}