{
  "id": "1604.01934",
  "version": "v1",
  "published": "2016-04-07T09:29:55.000Z",
  "updated": "2016-04-07T09:29:55.000Z",
  "title": "Fullerene graphs of small diameter",
  "authors": [
    "Diego Nicodemos",
    "Matěj Stehlík"
  ],
  "categories": [
    "math.CO"
  ],
  "abstract": "A fullerene graph is a cubic bridgeless plane graph with only pentagonal and hexagonal faces. We exhibit an infinite family of fullerene graphs of diameter $\\sqrt{4n/3}$, where $n$ is the number of vertices. This disproves a conjecture of Andova and \\v{S}krekovski [MATCH Commun. Math. Comput. Chem. 70 (2013) 205-220], who conjectured that every fullerene graph on $n$ vertices has diameter at least $\\lfloor \\sqrt{5n/3}\\rfloor-1$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-04-07T09:29:55.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "fullerene graph",
      "small diameter",
      "cubic bridgeless plane graph",
      "hexagonal faces",
      "match commun"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2016arXiv160401934N"
    }
  }
}