### Abstract

A pebbling move on a weighted graph removes some pebbles at a vertex and adds one pebble at an adjacent vertex. The number of pebbles removed is the weight of the edge connecting the vertices. A vertex is reachable from a pebble distribution if it is possible to move a pebble to that vertex using pebbling moves. The pebbling number of a weighted graph is the smallest number m needed to guarantee that any vertex is reachable from any pebble distribution of m pebbles. Regular pebbling problems on unweighted graphs are special cases when the weight on every edge is 2. A regular pebbling problem often simplifies to a pebbling problem on a simpler weighted graph. We present an algorithm to find the pebbling number of weighted graphs. We use this algorithm together with graph simplifications to find the regular pebbling number of all connected graphs with at most nine vertices.

Original language | English (US) |
---|---|

Pages (from-to) | 221-244 |

Number of pages | 24 |

Journal | Journal of Graph Algorithms and Applications |

Volume | 14 |

Issue number | 2 |

DOIs | |

State | Published - 2010 |

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### ASJC Scopus subject areas

- Theoretical Computer Science
- Computer Science(all)
- Geometry and Topology
- Computer Science Applications
- Computational Theory and Mathematics

### Cite this

**A graph pebbling algorithm on weighted graphs.** / Sieben, Nandor.

Research output: Contribution to journal › Article

*Journal of Graph Algorithms and Applications*, vol. 14, no. 2, pp. 221-244. https://doi.org/10.7155/jgaa.00205

}

TY - JOUR

T1 - A graph pebbling algorithm on weighted graphs

AU - Sieben, Nandor

PY - 2010

Y1 - 2010

N2 - A pebbling move on a weighted graph removes some pebbles at a vertex and adds one pebble at an adjacent vertex. The number of pebbles removed is the weight of the edge connecting the vertices. A vertex is reachable from a pebble distribution if it is possible to move a pebble to that vertex using pebbling moves. The pebbling number of a weighted graph is the smallest number m needed to guarantee that any vertex is reachable from any pebble distribution of m pebbles. Regular pebbling problems on unweighted graphs are special cases when the weight on every edge is 2. A regular pebbling problem often simplifies to a pebbling problem on a simpler weighted graph. We present an algorithm to find the pebbling number of weighted graphs. We use this algorithm together with graph simplifications to find the regular pebbling number of all connected graphs with at most nine vertices.

AB - A pebbling move on a weighted graph removes some pebbles at a vertex and adds one pebble at an adjacent vertex. The number of pebbles removed is the weight of the edge connecting the vertices. A vertex is reachable from a pebble distribution if it is possible to move a pebble to that vertex using pebbling moves. The pebbling number of a weighted graph is the smallest number m needed to guarantee that any vertex is reachable from any pebble distribution of m pebbles. Regular pebbling problems on unweighted graphs are special cases when the weight on every edge is 2. A regular pebbling problem often simplifies to a pebbling problem on a simpler weighted graph. We present an algorithm to find the pebbling number of weighted graphs. We use this algorithm together with graph simplifications to find the regular pebbling number of all connected graphs with at most nine vertices.

UR - http://www.scopus.com/inward/record.url?scp=80051536949&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=80051536949&partnerID=8YFLogxK

U2 - 10.7155/jgaa.00205

DO - 10.7155/jgaa.00205

M3 - Article

VL - 14

SP - 221

EP - 244

JO - Journal of Graph Algorithms and Applications

JF - Journal of Graph Algorithms and Applications

SN - 1526-1719

IS - 2

ER -