### 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 rubbling number 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 give bounds for rubbling and optimal rubbling numbers.

Original language | English (US) |
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Pages (from-to) | 487-492 |

Number of pages | 6 |

Journal | Electronic Notes in Discrete Mathematics |

Volume | 38 |

DOIs | |

State | Published - Dec 1 2011 |

### Keywords

- Bounded diameter
- Pebbling
- Rubbling

### ASJC Scopus subject areas

- Discrete Mathematics and Combinatorics
- Applied Mathematics