{
  "id": "2111.04869",
  "version": "v3",
  "published": "2021-11-08T23:27:18.000Z",
  "updated": "2022-01-25T07:40:31.000Z",
  "title": "Lin-Lu-Yau curvature and diameter of amply regular graphs",
  "authors": [
    "Xintian Li",
    "Shiping Liu"
  ],
  "comment": "5 pages",
  "journal": "J. Univ. Sci. Tech. China 51 (2021), no. 12, 889-893",
  "doi": "10.52396/JUST-2021-0232",
  "categories": [
    "math.CO",
    "math.DG"
  ],
  "abstract": "By Hall's marriage theorem, we study lower bounds of the Lin-Lu-Yau curvature of amply regular graphs with girth $3$ or $4$ under different parameter restrictions. As a consequence, we show that each conference graph has positive Lin-Lu-Yau curvature. Our approach also provides a geometric proof of a classical diameter estimate for amply regular graphs in the case of girth $4$ and some special cases of girth $3$.",
  "revisions": [
    {
      "version": "v3",
      "updated": "2022-01-25T07:40:31.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "amply regular graphs",
      "halls marriage theorem",
      "study lower bounds",
      "conference graph",
      "classical diameter estimate"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 5,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}