Local Symmetries of Symmetrical Cayley Maps
Date of Award
Doctor of Philosophy
Dr. John Martino
Dr. Terrell Hodge
Dr. Arthur White
Dr. Joseph Buckley
Graphs, groups, and surfaces are all subjects of study in topological graph theory, using techniques and principles from the disciplines of graph theory, algebra, and topology. A Cayley graph provides a graphical representation of a ¯nite group and a ¯xed generating set for the group; a Cayley map is a two-cell imbedding into a surface of a Cayley graph such that labeled outward-directed darts occur in the same sequence at each vertex. A dart is a directed edge. In this work, we generalize Cayley maps to allow two-cell imbeddings of graphs with loops and multiple edges.
Smith, Paula T., "Local Symmetries of Symmetrical Cayley Maps" (2002). Dissertations. 3150.