{
  "id": "0801.1483",
  "version": "v2",
  "published": "2008-01-09T18:26:48.000Z",
  "updated": "2009-08-11T10:14:29.000Z",
  "title": "On k-resonant fullerene graphs",
  "authors": [
    "Dong Ye",
    "Zhongbin Qi",
    "Heping Zhang"
  ],
  "comment": "26 pages; 29 figures",
  "journal": "SIAM J. DISCRETE MATH. Vol. 23 (2009) pp. 1023",
  "categories": [
    "math.CO"
  ],
  "abstract": "A fullerene graph $F$ is a 3-connected plane cubic graph with exactly 12 pentagons and the remaining hexagons. Let $M$ be a perfect matching of $F$. A cycle $C$ of $F$ is $M$-alternating if the edges of $C$ appear alternately in and off $M$. 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 all hexagons in $\\mathcal H$ are $M$-alternating. A fullerene graph $F$ is $k$-resonant if any $i$ ($0\\leq i \\leq k$) disjoint hexagons of $F$ form a resonant pattern. In this paper, we prove that every hexagon of a fullerene graph is resonant and all leapfrog fullerene graphs are 2-resonant. Further, we show that a 3-resonant fullerene graph has at most 60 vertices and construct all nine 3-resonant fullerene graphs, which are also $k$-resonant for every integer $k>3$. Finally, sextet polynomials of the 3-resonant fullerene graphs are computed.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2009-08-11T10:14:29.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05C70",
      "05C90"
    ],
    "keywords": [
      "k-resonant fullerene graphs",
      "disjoint hexagons",
      "plane cubic graph",
      "leapfrog fullerene graphs",
      "resonant pattern"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 26,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2008arXiv0801.1483Y"
    }
  }
}