Classes of arrangement graphs in three dimensions
Date
2005
Authors
Nickle, Elspeth J.
University of Lethbridge. Faculty of Arts and Science
Journal Title
Journal ISSN
Volume Title
Publisher
Lethbridge, Alta. : University of Lethbridge, Faculty of Arts and Science, 2005
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.
Description
x, 89 leaves : ill. (some col.) ; 29 cm
Keywords
Graph theory , Computer graphics , Geometrical constructions , Graphic methods , Dissertations, Academic