### Abstract

A pebbling move on a graph consists of taking two pebbles off of one vertex and placing one pebble on an adjacent vertex. In the traditional pebbling problem we try to reach a specified vertex of the graph by a sequence of pebbling moves. In this paper we investigate the case when every vertex of the graph must end up with at least one pebble after a series of pebbling moves. The cover pebbling number of a graph is the minimum number of pebbles such that however the pebbles are initially placed on the vertices of the graph we can eventually put a pebble on every vertex simultaneously. We find the cover pebbling numbers of trees and some other graphs. We also consider the more general problem where (possibly different) given numbers of pebbles are required for the vertices.

Original language | English |
---|---|

Pages (from-to) | 15-23 |

Number of pages | 9 |

Journal | Discrete Mathematics |

Volume | 296 |

Issue number | 1 |

DOIs | |

Publication status | Published - Jun 28 2005 |

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### Keywords

- Coverable
- Graph
- Pebbling

### ASJC Scopus subject areas

- Discrete Mathematics and Combinatorics
- Theoretical Computer Science

### Cite this

*Discrete Mathematics*,

*296*(1), 15-23. https://doi.org/10.1016/j.disc.2005.03.009

**The cover pebbling number of graphs.** / Crull, Betsy; Cundiff, Tammy; Feltman, Paul; Hurlbert, Glenn H.; Pudwell, Lara; Szaniszlo, Zsuzsanna; Tuza, Z.

Research output: Contribution to journal › Article

*Discrete Mathematics*, vol. 296, no. 1, pp. 15-23. https://doi.org/10.1016/j.disc.2005.03.009

}

TY - JOUR

T1 - The cover pebbling number of graphs

AU - Crull, Betsy

AU - Cundiff, Tammy

AU - Feltman, Paul

AU - Hurlbert, Glenn H.

AU - Pudwell, Lara

AU - Szaniszlo, Zsuzsanna

AU - Tuza, Z.

PY - 2005/6/28

Y1 - 2005/6/28

N2 - A pebbling move on a graph consists of taking two pebbles off of one vertex and placing one pebble on an adjacent vertex. In the traditional pebbling problem we try to reach a specified vertex of the graph by a sequence of pebbling moves. In this paper we investigate the case when every vertex of the graph must end up with at least one pebble after a series of pebbling moves. The cover pebbling number of a graph is the minimum number of pebbles such that however the pebbles are initially placed on the vertices of the graph we can eventually put a pebble on every vertex simultaneously. We find the cover pebbling numbers of trees and some other graphs. We also consider the more general problem where (possibly different) given numbers of pebbles are required for the vertices.

AB - A pebbling move on a graph consists of taking two pebbles off of one vertex and placing one pebble on an adjacent vertex. In the traditional pebbling problem we try to reach a specified vertex of the graph by a sequence of pebbling moves. In this paper we investigate the case when every vertex of the graph must end up with at least one pebble after a series of pebbling moves. The cover pebbling number of a graph is the minimum number of pebbles such that however the pebbles are initially placed on the vertices of the graph we can eventually put a pebble on every vertex simultaneously. We find the cover pebbling numbers of trees and some other graphs. We also consider the more general problem where (possibly different) given numbers of pebbles are required for the vertices.

KW - Coverable

KW - Graph

KW - Pebbling

UR - http://www.scopus.com/inward/record.url?scp=19944389625&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=19944389625&partnerID=8YFLogxK

U2 - 10.1016/j.disc.2005.03.009

DO - 10.1016/j.disc.2005.03.009

M3 - Article

AN - SCOPUS:19944389625

VL - 296

SP - 15

EP - 23

JO - Discrete Mathematics

JF - Discrete Mathematics

SN - 0012-365X

IS - 1

ER -