{"id":{"repo_id":"wfu","oai_identifier":"oai:wakespace.lib.wfu.edu:10339/39310"},"canonical_url":"https://search.dev.ndltd.org/etd/wfu/oai:wakespace.lib.wfu.edu:10339/39310","repository":{"repo_id":"wfu","name":"Wake Forest University","base_url":"https://wakespace.lib.wfu.edu/oai/request"},"display":{"title":"Generalizations and Variations on Graph Pebbling","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.","abstract_html":"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.","abstract_has_math":false,"creators":["Barnett, Joel Andrew"],"institution":"Wake Forest University","degree_name":null,"degree_level":null,"degree_discipline":null,"degree_department":null,"school":null,"contributors":[],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2014,"date_issued":"2014","date_published":"2014","updated_at":"2026-07-27T22:01:46Z","subjects":["graph pebbling"],"languages":["en"],"rights":[],"rights_urls":[],"identifier_entries":[]},"links":{"outbound_url":"http://hdl.handle.net/10339/39310","outbound_label":"Handle","outbound_source":"dc:identifier.uri"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:creator","label":"Author","values":["Barnett, Joel Andrew"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date.accessioned","label":"Dc Date Accessioned","values":["2014-07-10T08:35:39Z"]},{"key":"dc:date.available","label":"Dc Date Available","values":["2014-07-10T08:35:39Z"]},{"key":"dc:date.issued","label":"Date","values":["2014"]},{"key":"dc:publisher","label":"Institution","values":["Wake Forest University"]},{"key":"dc:type","label":"Dc Type","values":["Thesis"]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["graph pebbling"]}]},{"id":"language_rights","label":"Language and Rights","entries":[{"key":"dc:language.iso","label":"Language (ISO)","values":["en"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier.uri","label":"Identifier URI","values":["http://hdl.handle.net/10339/39310"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description.abstract","label":"Abstract","values":["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."]},{"key":"dc:title","label":"Title","values":["Generalizations and Variations on Graph Pebbling"]}]}],"canonical_facts":{"dc:creator":["Barnett, Joel Andrew"],"dc:date.accessioned":["2014-07-10T08:35:39Z"],"dc:date.available":["2014-07-10T08:35:39Z"],"dc:date.issued":["2014"],"dc:description.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."],"dc:identifier.uri":["http://hdl.handle.net/10339/39310"],"dc:language.iso":["en"],"dc:publisher":["Wake Forest University"],"dc:subject":["graph pebbling"],"dc:title":["Generalizations and Variations on Graph Pebbling"],"dc:type":["Thesis"]},"updated_at":"2026-07-27T22:01:46Z"}