{
  "abstract": "So conjectured that, for a fixed positive integer n, the ordinary adjacency spectrum of an integral circulant graph of order n determines its divisor set. We prove this for graphs of order p to the power a times q, where p and q are primes with p less than q and a is at least one. To handle coincident eigenvalues arising from distinct greatest-common-divisor classes, we use a spectral counting measure. For connected graphs, an exact identity recovers the part of the divisor set consisting of one and q, when present, together with the counting measure for a graph of order p to the power a minus one times q. Strong induction and decomposition into connected components then recover the full divisor set, including the case p equals two and disconnected graphs.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.20072",
  "author_total": 2,
  "authors": [
    {
      "name": "Jianwei Jiang"
    },
    {
      "name": "Chunhua Yang"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/6914bz8s1n2n6.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.20072",
  "fulltext_url": null,
  "id": "6914bz8s1n2n6",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.20072",
  "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"
    ],
    [
      "openalex",
      "2608|Graph theory and applications"
    ]
  ],
  "openalex": "W7213609949",
  "pdf_url": "https://arxiv.org/pdf/2609.20072",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-17",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/6914bz8s1n2n6.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:22:23Z",
      "native_id": "2609.20072",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.20072"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CO",
      "subfield": "combinatorics"
    }
  ],
  "title": "So's Conjecture for Integral Circulant Graphs of Order p^aq",
  "title_text": "So's Conjecture for Integral Circulant Graphs of Order p^aq",
  "type": "preprint",
  "updated_at": "2026-10-30T12:22:23Z",
  "url": "https://research.draconitic.com/paper/6914bz8s1n2n6",
  "venue": "arXiv",
  "versions": []
}