{
  "id": "1411.0923",
  "version": "v1",
  "published": "2014-11-04T14:33:31.000Z",
  "updated": "2014-11-04T14:33:31.000Z",
  "title": "The Optimal Rubbling Number of Ladders, Prisms and Möbius-ladders",
  "authors": [
    "Gyula Y. Katona",
    "László Papp"
  ],
  "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 each 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 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 optimal rubbling number of ladders ($P_n\\square P_2$), prisms ($C_n\\square P_2$) and M\\\"oblus-ladders.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2014-11-04T14:33:31.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05C85",
      "05C57",
      "G.2.2"
    ],
    "keywords": [
      "optimal rubbling number",
      "möbius-ladders",
      "pebble distribution",
      "adjacent vertex",
      "additional move"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2014arXiv1411.0923K"
    }
  }
}