Classes of arrangement graphs in three dimensions
Nickle, Elspeth J.
University of Lethbridge. Faculty of Arts and Science
Lethbridge, Alta. : University of Lethbridge, Faculty of Arts and Science, 2005
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
Graph theory , Computer graphics , Geometrical constructions , Graphic methods , Dissertations, Academic