{
  "id": "1609.07133",
  "version": "v1",
  "published": "2016-09-22T19:57:48.000Z",
  "updated": "2016-09-22T19:57:48.000Z",
  "title": "Strongly regular graphs from orthogonal groups $O^+(6,2)$ and $O^-(6,2)$",
  "authors": [
    "Dean Crnković",
    "Sanja Rukavina",
    "Andrea Švob"
  ],
  "comment": "12 pages",
  "categories": [
    "math.CO"
  ],
  "abstract": "In this paper we construct all strongly regular graphs, with at most 550 vertices, admitting a transitive action of the orthogonal group $O^+(6,2)$ or $O^-(6,2)$. Consequently, we prove the existence of strongly regular graphs with parameters (216,40,4,8) and (540,187,58,68). Further, we show that under certain conditions an orbit matrix $M$ of a strongly regular graph $\\Gamma$ can be used to define a new strongly regular graph $\\widetilde{\\Gamma}$, where the vertices of the graph $\\widetilde{\\Gamma}$ correspond to the orbits of $\\Gamma$ (the rows of $M$). We show that some of the obtained graphs are related to each other, meaning that one can be constructed from an orbit matrix of the other.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-09-22T19:57:48.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05E30",
      "05E18"
    ],
    "keywords": [
      "strongly regular graph",
      "orthogonal group",
      "orbit matrix",
      "conditions",
      "transitive action"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 12,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}