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Generalizations and Variations on Graph Pebbling

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title
Generalizations and Variations on Graph Pebbling
author
Barnett, Joel Andrew
abstract
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.
subject
graph pebbling
graph theory
contributor
Mason, Sarah K (committee chair)
Howards, Hugh N (committee member)
Parsley, Robert J (committee member)
date
2014-07-10T08:35:39Z (accessioned)
2014-07-10T08:35:39Z (available)
2014 (issued)
degree
Mathematics (discipline)
identifier
http://hdl.handle.net/10339/39310 (uri)
language
en (iso)
publisher
Wake Forest University
type
Thesis

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