Award Date

December 2017

Degree Type

Thesis

Degree Name

Master of Science (MS)

Department

Mathematical Sciences

First Committee Member

Michelle Robinette

Second Committee Member

Ebrahim Salehi

Third Committee Member

Peter Shiue

Fourth Committee Member

Laxmi Gewali

Number of Pages

52

Abstract

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.

Disciplines

Mathematics

Language

English


Included in

Mathematics Commons

Share

COinS