{
  "id": "2308.00340",
  "version": "v1",
  "published": "2023-08-01T07:25:18.000Z",
  "updated": "2023-08-01T07:25:18.000Z",
  "title": "A short note on cospectral and integral chain graphs for Seidel matrix",
  "authors": [
    "Santanu Mandal"
  ],
  "categories": [
    "math.CO"
  ],
  "abstract": "In this brief communication, we investigate the cospectral as well integral chain graphs for Seidel matrix, a key component to study the structural properties of equiangular lines in space. We derive a formula that allows to generate an infinite number of inequivalent chain graphs with identical spectrum. In addition, we obtain a family of Seidel integral chain graphs. This contrapositively answers a problem posed by Greaves [\"Equiangular line systems and switching classes containing regular graphs\", Linear Algebra Appl., (2018)] (\"Does every Seidel matrix with precisely three distinct rational eigenvalues contain a regular graph in its switching class?\"). Our observation is- \"no\".",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-08-01T07:25:18.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05C50"
    ],
    "keywords": [
      "seidel matrix",
      "short note",
      "classes containing regular graphs",
      "cospectral",
      "seidel integral chain graphs"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}