Local Symmetries of Symmetrical Cayley Maps

Date of Award


Degree Name

Doctor of Philosophy



First Advisor

Dr. John Martino

Second Advisor

Dr. Terrell Hodge

Third Advisor

Dr. Arthur White

Fourth Advisor

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.


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Access Setting

Dissertation-Open Access

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