{
  "id": "1211.5640",
  "version": "v1",
  "published": "2012-11-24T03:15:00.000Z",
  "updated": "2012-11-24T03:15:00.000Z",
  "title": "2-Resonant fullerenes",
  "authors": [
    "Rui Yang",
    "Heping Zhang"
  ],
  "comment": "34 pages, 25 figures",
  "categories": [
    "math.CO"
  ],
  "abstract": "A fullerene graph $F$ is a planar cubic graph with exactly 12 pentagonal faces and other hexagonal faces. A set $\\mathcal{H}$ of disjoint hexagons of $F$ is called a resonant pattern (or sextet pattern) if $F$ has a perfect matching $M$ such that every hexagon in $\\mathcal{H}$ is $M$-alternating. $F$ is said to be $k$-resonant if any $i$ ($0\\leq i\\leq k$) disjoint hexagons of $F$ form a resonant pattern. It was known that each fullerene graph is 1-resonant and all 3-resonant fullerenes are only the nine graphs. In this paper, we show that the fullerene graphs which do not contain the subgraph $L$ or $R$ as illustrated in Fig. 1 are 2-resonant except for the specific eleven graphs. This result implies that each IPR fullerene is 2-resonant.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2012-11-24T03:15:00.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05C10",
      "05C70",
      "05C90",
      "92E10"
    ],
    "keywords": [
      "fullerene graph",
      "disjoint hexagons",
      "planar cubic graph",
      "ipr fullerene",
      "pentagonal faces"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 34,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2012arXiv1211.5640Y"
    }
  }
}