{
  "id": "1806.10068",
  "version": "v1",
  "published": "2018-06-26T15:42:47.000Z",
  "updated": "2018-06-26T15:42:47.000Z",
  "title": "Nonsingularity of adjacency matrices of random $r$-regular graphs",
  "authors": [
    "Hoi H. Nguyen",
    "Melanie Matchett Wood"
  ],
  "categories": [
    "math.PR",
    "math.CO"
  ],
  "abstract": "We prove that the adjacency matrices of uniform random r-regular graphs on n vertices are asymptotically almost surely nonsingular for even n. We use recent mixing results of M\\'esz\\'aros for adjacency matrices of certain random r-regular multi-graphs and results of the second author on the moment problem for random finite abelian groups.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-06-26T15:42:47.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "adjacency matrices",
      "uniform random r-regular graphs",
      "nonsingularity",
      "random finite abelian groups",
      "random r-regular multi-graphs"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}