# The cover pebbling number of graphs

Betsy Crull, Tammy Cundiff, Paul Feltman, Glenn H. Hurlbert, Lara Pudwell, Zsuzsanna Szaniszlo, Zsolt Tuza

Research output: Contribution to journalArticle

22 Citations (Scopus)

### 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 15-23 9 Discrete Mathematics 296 1 https://doi.org/10.1016/j.disc.2005.03.009 Published - Jun 28 2005

• Coverable
• Graph
• Pebbling

### ASJC Scopus subject areas

• Theoretical Computer Science
• Discrete Mathematics and Combinatorics

• ## Cite this

Crull, B., Cundiff, T., Feltman, P., Hurlbert, G. H., Pudwell, L., Szaniszlo, Z., & Tuza, Z. (2005). The cover pebbling number of graphs. Discrete Mathematics, 296(1), 15-23. https://doi.org/10.1016/j.disc.2005.03.009