{
  "id": "2102.11989",
  "version": "v1",
  "published": "2021-02-24T00:11:20.000Z",
  "updated": "2021-02-24T00:11:20.000Z",
  "title": "Maximality of Seidel matrices and switching roots of graphs",
  "authors": [
    "Meng-Yue Cao",
    "Jack H. Koolen",
    "Akihiro Munemasa",
    "Kiyoto Yoshino"
  ],
  "comment": "18 pages",
  "categories": [
    "math.CO"
  ],
  "abstract": "In this paper, we discuss maximality of Seidel matrices with a fixed largest eigenvalue. We present a classification of maximal Seidel matrices of largest eigenvalue $3$, which gives a classification of maximal equiangular lines in a Euclidean space with angle $\\arccos1/3$. Motivated by the maximality of the exceptional root system $E_8$, we define strong maximality of a Seidel matrix, and show that every Seidel matrix achieving the absolute bound is strongly maximal.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2021-02-24T00:11:20.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05C50",
      "05C22"
    ],
    "keywords": [
      "seidel matrix",
      "switching roots",
      "define strong maximality",
      "exceptional root system",
      "maximal equiangular lines"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 18,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}