{
  "abstract": "Let $G$ be a finite group and $H$ be a subgroup of $G$. In our earlier work, we proved that the quasi-strongly regular Cayley graph $Γ_H(G)$ is integral whenever $H$ is normal in $G$, and raised the question of whether the converse also holds. In this paper, we answer this question affirmatively. We prove that if $Γ_H(G)$ is integral, then $H$ must be a normal subgroup of $G$. Consequently, $Γ_H(G)$ is integral if and only if $H\\lhd G$. Our proof uses the irreducible representations of $G$ and the dimensions of their $H$-fixed subspaces. For a non-normal subgroup $H$, we construct a two-dimensional invariant subspace of a suitable representation operator and show that the corresponding eigenvalues are irrational.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2611.06581",
  "author_total": 2,
  "authors": [
    {
      "name": "Sauvik Poddar"
    },
    {
      "name": "Sucharita Biswas"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/1pa0ytd7r7h1v.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2611.06581",
  "fulltext_url": null,
  "id": "1pa0ytd7r7h1v",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2611.06581",
  "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": null,
  "pdf_url": "https://arxiv.org/pdf/2611.06581",
  "pmcid": null,
  "pmid": null,
  "published": "2026-11-04",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/1pa0ytd7r7h1v.ris",
  "sources": [
    {
      "first_seen": "2026-11-05T15:21:00Z",
      "native_id": "2611.06581",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2611.06581"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.GR",
      "subfield": "algebra-number-theory"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.CO",
      "subfield": "combinatorics"
    }
  ],
  "title": "A characterization of a family of integral Cayley graphs",
  "title_text": "A characterization of a family of integral Cayley graphs",
  "type": "preprint",
  "updated_at": "2026-11-09T00:20:30Z",
  "url": "https://research.draconitic.com/paper/1pa0ytd7r7h1v",
  "venue": "arXiv",
  "versions": []
}