{
  "id": "0707.4256",
  "version": "v1",
  "published": "2007-07-28T19:32:08.000Z",
  "updated": "2007-07-28T19:32:08.000Z",
  "title": "Rubbling and Optimal Rubbling of Graphs",
  "authors": [
    "Christopher Belford",
    "Nandor Sieben"
  ],
  "comment": "14 pages",
  "categories": [
    "math.CO"
  ],
  "abstract": "A pebbling move on a graph removes two pebbles at a vertex and adds one pebble at an adjacent vertex. Rubbling is a version of pebbling where an additional move is allowed. In this new move one pebble is removed at vertices v and w adjacent to a vertex u and an extra pebble is added at vertex u. A vertex is reachable from a pebble distribution if it is possible to move a pebble to that vertex using rubbling moves. The rubbling number of a graph is the smallest number m needed to guarantee that any vertex is reachable from any pebble distribution of m pebbles. The optimal rubbling number is the smallest number m needed to guarantee a pebble distribution of m pebbles from which any vertex is reachable. We determine the rubbling and optimal rubbling number of some families of graphs including cycles.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2007-07-28T19:32:08.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "pebble distribution",
      "optimal rubbling number",
      "smallest number",
      "additional move",
      "graph removes"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 14,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2007arXiv0707.4256B"
    }
  }
}