{
  "id": "1904.04870",
  "version": "v1",
  "published": "2019-04-09T19:03:44.000Z",
  "updated": "2019-04-09T19:03:44.000Z",
  "title": "Determinants of Seidel matrices and a conjecture of Ghorbani",
  "authors": [
    "Douglas Rizzolo"
  ],
  "categories": [
    "math.CO",
    "math.PR"
  ],
  "abstract": "Let $G_n$ be a simple graph on $V_n=\\{v_1,\\dots, v_n\\}$. The Seidel matrix $S(G_n)$ of $G_n$ is the $n\\times n$ matrix whose $(ij)$'th entry, for $i\\neq j$ is $-1$ if $v_i\\sim v_j$ and $1$ otherwise, and whose diagonal entries are $0$. We show that the proportion of simple graphs $G_n$ such that $\\det(S(G_n))\\geq n-1$ tends to one as $n$ tends to infinity.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-04-09T19:03:44.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05C50"
    ],
    "keywords": [
      "seidel matrix",
      "determinants",
      "simple graph",
      "conjecture"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}