{"id":{"repo_id":"wfu","oai_identifier":"oai:wakespace.lib.wfu.edu:10339/90759"},"canonical_url":"https://search.dev.ndltd.org/etd/wfu/oai:wakespace.lib.wfu.edu:10339/90759","repository":{"repo_id":"wfu","name":"Wake Forest University","base_url":"https://wakespace.lib.wfu.edu/oai/request"},"display":{"title":"Edge Labelings on the Partially Ordered Set of Non-Crossing Bonds","abstract":"Let G be a graph with a finite vertex set and edge set. A bond of G is a spanning subgraph of G whose connected components are induced. This collection of bonds form a partially ordered set which is also a lattice. This lattice has what is known as an ER-labeling. We explore a new subposet of this lattice which we call the “non-crossing bond poset” for all graphs finite graphs. Then we aim to show when this subposet has the desired ER-labeling and when it does not. This paper will focus on what the bond lattice of a graph is, examples of when the non-crossing bond poset has an ER-labeling and when it does not, and the classification of all graphs whose non-crossing bond poset has an ER-labeling. Once such graphs have been found, we then attempt to find the characteristic polynomials of such posets.","abstract_html":"Let G be a graph with a finite vertex set and edge set. A bond of G is a spanning subgraph of G whose connected components are induced. This collection of bonds form a partially ordered set which is also a lattice. This lattice has what is known as an ER-labeling. We explore a new subposet of this lattice which we call the “non-crossing bond poset” for all graphs finite graphs. Then we aim to show when this subposet has the desired ER-labeling and when it does not. This paper will focus on what the bond lattice of a graph is, examples of when the non-crossing bond poset has an ER-labeling and when it does not, and the classification of all graphs whose non-crossing bond poset has an ER-labeling. Once such graphs have been found, we then attempt to find the characteristic polynomials of such posets.","abstract_has_math":false,"creators":["Farmer, Charles Matthew"],"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":2018,"date_issued":"2018","date_published":"2018","updated_at":"2026-07-27T22:02:23Z","subjects":[],"languages":["en"],"rights":[],"rights_urls":[],"identifier_entries":[]},"links":{"outbound_url":"http://hdl.handle.net/10339/90759","outbound_label":"Handle","outbound_source":"dc:identifier.uri"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:creator","label":"Author","values":["Farmer, Charles Matthew"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date.accessioned","label":"Dc Date Accessioned","values":["2018-05-24T08:36:19Z"]},{"key":"dc:date.available","label":"Dc Date Available","values":["2018-05-24T08:36:19Z"]},{"key":"dc:date.issued","label":"Date","values":["2018"]},{"key":"dc:publisher","label":"Institution","values":["Wake Forest University"]},{"key":"dc:type","label":"Dc Type","values":["Thesis"]}]},{"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/10339/90759"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description.abstract","label":"Abstract","values":["Let G be a graph with a finite vertex set and edge set. A bond of G is a spanning subgraph of G whose connected components are induced. This collection of bonds form a partially ordered set which is also a lattice. This lattice has what is known as an ER-labeling. We explore a new subposet of this lattice which we call the “non-crossing bond poset” for all graphs finite graphs. Then we aim to show when this subposet has the desired ER-labeling and when it does not. This paper will focus on what the bond lattice of a graph is, examples of when the non-crossing bond poset has an ER-labeling and when it does not, and the classification of all graphs whose non-crossing bond poset has an ER-labeling. Once such graphs have been found, we then attempt to find the characteristic polynomials of such posets."]},{"key":"dc:title","label":"Title","values":["Edge Labelings on the Partially Ordered Set of Non-Crossing Bonds"]}]}],"canonical_facts":{"dc:creator":["Farmer, Charles Matthew"],"dc:date.accessioned":["2018-05-24T08:36:19Z"],"dc:date.available":["2018-05-24T08:36:19Z"],"dc:date.issued":["2018"],"dc:description.abstract":["Let G be a graph with a finite vertex set and edge set. A bond of G is a spanning subgraph of G whose connected components are induced. This collection of bonds form a partially ordered set which is also a lattice. This lattice has what is known as an ER-labeling. We explore a new subposet of this lattice which we call the “non-crossing bond poset” for all graphs finite graphs. Then we aim to show when this subposet has the desired ER-labeling and when it does not. This paper will focus on what the bond lattice of a graph is, examples of when the non-crossing bond poset has an ER-labeling and when it does not, and the classification of all graphs whose non-crossing bond poset has an ER-labeling. Once such graphs have been found, we then attempt to find the characteristic polynomials of such posets."],"dc:identifier.uri":["http://hdl.handle.net/10339/90759"],"dc:language.iso":["en"],"dc:publisher":["Wake Forest University"],"dc:title":["Edge Labelings on the Partially Ordered Set of Non-Crossing Bonds"],"dc:type":["Thesis"]},"updated_at":"2026-07-27T22:02:23Z"}