{
  "id": "2504.19560",
  "version": "v2",
  "published": "2025-04-28T08:10:00.000Z",
  "updated": "2025-05-07T07:29:36.000Z",
  "title": "Strongly regular graphs in hyperbolic quadrics",
  "authors": [
    "Antonio Cossidente",
    "Jan De Beule",
    "Giuseppe Marino",
    "Francesco Pavese",
    "Valentino Smaldore"
  ],
  "categories": [
    "math.CO"
  ],
  "abstract": "Let $Q^+(2n+1,q)$ be a hyperbolic quadric of $\\PG(2n+1,q)$. Fix a generator $\\Pi$ of the quadric. Define $\\cG_n$ as the graph with vertex set the points of $Q^+(2n+1,q)\\setminus \\Pi$ and two vertices adjacent if they either span a secant to $Q^+(2n+1,q)$ or a line contained in $Q^+(2n+1,q)$ meeting $\\Pi$ non-trivially. Then such a construction defines a strongly regular graph, which is the complement of a (non-induced) subgraph of the collinearity graph of $Q^+(2n+1,q)$. In this paper, we directly compute the parameters of $\\cG_n$, which is cospectral, when $q=2$, to the tangent graph $NO^+(2n+2,2)$, but it is non-isomorphic for $n\\geq3$. We also prove the non-isomorphism by analyzing the case of the quadric $Q^+(7,2)$.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2025-05-07T07:29:36.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "51E20",
      "05E30"
    ],
    "keywords": [
      "strongly regular graph",
      "hyperbolic quadric",
      "vertices adjacent",
      "tangent graph",
      "construction defines"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}