{
  "id": "2004.10038",
  "version": "v1",
  "published": "2020-04-21T14:20:54.000Z",
  "updated": "2020-04-21T14:20:54.000Z",
  "title": "On the spectral gap and the diameter of Cayley graphs",
  "authors": [
    "Ilya D. Shkredov"
  ],
  "comment": "22 pages",
  "categories": [
    "math.CO",
    "math.NT"
  ],
  "abstract": "We obtain a new bound connecting the first non--trivial eigenvalue of the Laplace operator of a graph and the diameter of the graph, which is effective for graphs with small diameter or for graphs, having the number of maximal paths comparable to the expectation.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-04-21T14:20:54.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "cayley graphs",
      "spectral gap",
      "first non-trivial eigenvalue",
      "laplace operator",
      "small diameter"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 22,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}