Master of Science (MS)
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Determining the orientable surfaces on which a particular graph may be imbedded is a basic problem in the area of topological graph theory. We look at groups modeled by Cayley graphs. Imbedding Cayley graphs with symmetry is done using Cayley maps. It is of interest to find the average Cayley genus for a particular group and generating set for the group. We consider the group known as the generalized quaternions with generating set ∆, where ∆ contains two generators with order greater than two. We find a formula for the average Cayley genus of the generalized quaternions. Moreover, we determine a formula for the average Cayley genus of any finite group that can be generated by two generators with order greater than two. Finally, we find the average Cayley genus of a finite group with generating set consisting of three elements, two with order greater than two and one with order two.
University of Nevada, Las Vegas
Sturgeon, Dawn, "Average Cayley Genus for Groups with Two Generators of Order Greater Than Two" (2017). UNLV Theses, Dissertations, Professional Papers, and Capstones. 3173.
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