The cover pebbling number of graphs

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

Research output: Contribution to journalArticle

20 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 languageEnglish
Pages (from-to)15-23
Number of pages9
JournalDiscrete Mathematics
Volume296
Issue number1
DOIs
Publication statusPublished - Jun 28 2005

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Cover
Graph in graph theory
Vertex of a graph
Adjacent
Series

Keywords

  • Coverable
  • Graph
  • Pebbling

ASJC Scopus subject areas

  • Discrete Mathematics and Combinatorics
  • Theoretical Computer Science

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

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

In: Discrete Mathematics, Vol. 296, No. 1, 28.06.2005, p. 15-23.

Research output: Contribution to journalArticle

Crull, B, Cundiff, T, Feltman, P, Hurlbert, GH, Pudwell, L, Szaniszlo, Z & Tuza, Z 2005, 'The cover pebbling number of graphs', Discrete Mathematics, vol. 296, no. 1, pp. 15-23. https://doi.org/10.1016/j.disc.2005.03.009
Crull B, Cundiff T, Feltman P, Hurlbert GH, Pudwell L, Szaniszlo Z et al. The cover pebbling number of graphs. Discrete Mathematics. 2005 Jun 28;296(1):15-23. https://doi.org/10.1016/j.disc.2005.03.009
Crull, Betsy ; Cundiff, Tammy ; Feltman, Paul ; Hurlbert, Glenn H. ; Pudwell, Lara ; Szaniszlo, Zsuzsanna ; Tuza, Z. / The cover pebbling number of graphs. In: Discrete Mathematics. 2005 ; Vol. 296, No. 1. pp. 15-23.
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