Generalizations and Variations on Graph Pebbling

Graph pebbling involves determining the minimum number of pebbles needed so that regardless of the initial arrangement of pebbles on a graph, a pebble can be moved to any vertex using specified ``pebbling moves.'' This minimum number of pebbles is the pebbling number of a graph. We begin by making a brief exploration into path pebbling, which uses a sequence of pebbling moves instead of a single pebbling move. Returning to normal pebbling moves, we note that graph pebbling can be generalized by looking at a target distribution of pebbles, rather than just reaching one vertex with one pebble. We examine a contrast between pebbling on a labeled graph (where the target distribution is fixed) and an unlabeled graph (where the target distribution may be represented in multiple ways). We also seek to extend Jonas Sjostrand's Cover Pebbling Theorem to make calculating some pebbling numbers easier.

Grantor dc:publisher

Wake Forest University

Year dc:date.issued

2014

Author dc:creator

• Barnett, Joel Andrew

• graph pebbling

Language dc:language.iso

en

Handle dc:identifier.uri

http://hdl.handle.net/10339/39310

OAI identifier oai:identifier

oai:wakespace.lib.wfu.edu:10339/39310