Conditions for Weighted Cover Pebbling of Graphs
| dc.creator | Vuong, Annalies | |
| dc.creator | Wyckoff, M. Ian | |
| dc.date | 2004-10-18 | |
| dc.date.accessioned | 2026-07-07T05:13:24Z | |
| dc.date.available | 2026-07-07T05:13:24Z | |
| dc.description | In a graph G with a distribution of pebbles on its vertices, a pebbling move is the removal of two pebbles from one vertex and the addition of one pebble to an adjacent vertex. A weight function on G is a non-negative integer-valued function on the vertices of G. A distribution of pebbles on G covers a weight function if there exists a sequence of pebbling moves that gives a new distribution in which every vertex has at least as many pebbles as its weight. In this paper we give some necessary and some sufficient conditions for a distribution of pebbles to cover a given weight function on a connected graph G. As a corollary, we give a simple formulation for the `weighted cover pebbling number' of a weight function W and a connected graph G, defined by Crull et al. to be the smallest number m such that any distribution on G of m pebbles is a cover for W. Also, we prove a cover pebbling variant of Graham's Conjecture for pebbling. | |
| dc.description | 8 pages | |
| dc.identifier | https://arxiv.org/abs/math/0410410 | |
| dc.identifier | http://arxiv.org/abs/math/0410410 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/72932 | |
| dc.subject | Combinatorics | |
| dc.subject | 05C99, 05C35 | |
| dc.title | Conditions for Weighted Cover Pebbling of Graphs | |
| dc.type | text |