{
  "id": "1909.01703",
  "version": "v1",
  "published": "2019-09-04T11:39:24.000Z",
  "updated": "2019-09-04T11:39:24.000Z",
  "title": "A note on the optimal rubbling in ladders and prisms",
  "authors": [
    "Zheng-Jiang Xia",
    "Zhen-Mu Hong"
  ],
  "comment": "11 pages,3 figures, 2 tables",
  "categories": [
    "math.CO"
  ],
  "abstract": "A pebbling move on a graph G consists of the removal of two pebbles from one vertex and the placement of one pebble on an adjacent vertex. Rubbling is a version of pebbling where an additional move is allowed, which is also called the strict rubbling move. In this new move, one pebble each is removed from u and v adjacent to a vertex w, and one pebble is added on w. The optimal rubbling number of a graph G is the smallest number m, such that one pebble can be moved to every given vertex from some pebble distribution of m pebbles by a sequence of rubbling moves. In this paper, we give short proofs to determine the rubbling number of cycles and the optimal rubbling number of paths, cycles, ladders, prisms and Mobius-ladders.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-09-04T11:39:24.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05C99"
    ],
    "keywords": [
      "optimal rubbling number",
      "strict rubbling move",
      "additional move",
      "smallest number",
      "short proofs"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 11,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}