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. / x, 89 leaves : ill. (some col.) ; 29 cm
| Identifer | oai:union.ndltd.org:LACETR/oai:collectionscanada.gc.ca:ALU.w.uleth.ca/dspace#10133/632 |
| Date | January 2005 |
| Creators | Nickle, Elspeth J., University of Lethbridge. Faculty of Arts and Science |
| Contributors | Wismath, Stephen, Gaur, Daya |
| Publisher | Lethbridge, Alta. : University of Lethbridge, Faculty of Arts and Science, 2005, Faculty of Arts and Science, Department of Mathematics and Computer Science |
| Source Sets | Library and Archives Canada ETDs Repository / Centre d'archives des thèses électroniques de Bibliothèque et Archives Canada |
| Language | en_US |
| Detected Language | English |
| Type | Thesis |
| Relation | Thesis (University of Lethbridge. Faculty of Arts and Science) |
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