{"id":{"repo_id":"lethbridge","oai_identifier":"oai:opus.uleth.ca:10133/632"},"canonical_url":"https://search.dev.ndltd.org/etd/lethbridge/oai:opus.uleth.ca:10133/632","repository":{"repo_id":"lethbridge","name":"University of Lethbridge","base_url":"https://opus.uleth.ca/server/oai/request"},"display":{"title":"Classes of arrangement graphs in three dimensions","abstract":"A 3D arrangement graph G is the abstract graph induced by an arrangement of planes in general position where the intersection of any two planes forms a line of intersection and an intersection of three planes creates a point. The properties of three classes of arrangement graphs — four, five and six planes — are investigated. For graphs induced from six planes, specialized methods were developed to ensure all possible graphs were discovered. The main results are: the number of 3D arrangement graphs induced by four, five and six planes are one, one and 43 respectively; the three classes are Hamiltonian; and the 3D arrangement graphs created from four and five planes are planar but none of the graphs created from six planes are planar.","abstract_html":"A 3D arrangement graph G is the abstract graph induced by an arrangement of planes in general position where the intersection of any two planes forms a line of intersection and an intersection of three planes creates a point. The properties of three classes of arrangement graphs — four, five and six planes — are investigated. For graphs induced from six planes, specialized methods were developed to ensure all possible graphs were discovered. The main results are: the number of 3D arrangement graphs induced by four, five and six planes are one, one and 43 respectively; the three classes are Hamiltonian; and the 3D arrangement graphs created from four and five planes are planar but none of the graphs created from six planes are planar.","abstract_has_math":false,"creators":["Nickle, Elspeth J.","University of Lethbridge. Faculty of Arts and Science"],"institution":null,"degree_name":null,"degree_level":null,"degree_discipline":null,"degree_department":null,"school":null,"contributors":[],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2005,"date_issued":"2005","date_published":"2005","updated_at":"2026-07-27T20:02:23Z","subjects":["Graph theory","Computer graphics","Geometrical constructions","Graphic methods","Dissertations, Academic"],"languages":[],"rights":[],"rights_urls":[],"identifier_entries":[{"key":"dc:identifier","label":"Identifier","values":["hdl:10133/632"],"render_values":[{"text":"hdl:10133/632","href":null,"code":true}]}]},"links":{"outbound_url":null,"outbound_label":null,"outbound_source":null},"metadata_groups":[{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date.issued","label":"Date","values":["2005"]},{"key":"dc:type","label":"Dc Type","values":["Thesis"]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["Graph theory","Computer graphics","Geometrical constructions","Graphic methods","Dissertations, Academic"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["hdl:10133/632"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description.other","label":"Dc Description Other","values":["A 3D arrangement graph G is the abstract graph induced by an arrangement of planes in general position where the intersection of any two planes forms a line of intersection and an intersection of three planes creates a point. The properties of three classes of arrangement graphs — four, five and six planes — are investigated. For graphs induced from six planes, specialized methods were developed to ensure all possible graphs were discovered. The main results are: the number of 3D arrangement graphs induced by four, five and six planes are one, one and 43 respectively; the three classes are Hamiltonian; and the 3D arrangement graphs created from four and five planes are planar but none of the graphs created from six planes are planar."]},{"key":"dc:title","label":"Title","values":["Classes of arrangement graphs in three dimensions"]}]}],"canonical_facts":{"dc:date.issued":["2005"],"dc:description.other":["A 3D arrangement graph G is the abstract graph induced by an arrangement of planes in general position where the intersection of any two planes forms a line of intersection and an intersection of three planes creates a point. The properties of three classes of arrangement graphs — four, five and six planes — are investigated. For graphs induced from six planes, specialized methods were developed to ensure all possible graphs were discovered. The main results are: the number of 3D arrangement graphs induced by four, five and six planes are one, one and 43 respectively; the three classes are Hamiltonian; and the 3D arrangement graphs created from four and five planes are planar but none of the graphs created from six planes are planar."],"dc:identifier":["hdl:10133/632"],"dc:subject":["Graph theory","Computer graphics","Geometrical constructions","Graphic methods","Dissertations, Academic"],"dc:title":["Classes of arrangement graphs in three dimensions"],"dc:type":["Thesis"]},"updated_at":"2026-07-27T20:02:23Z"}