Date of Award

Spring 2021

Thesis Type

Open Access

Degree Name

Honors Bachelor of Arts

Department

Mathematics

Sponsor

Dr. Mark Anderson

Committee Member

Dr. Jay Yellen

Committee Member

Dr. Sheri Boyd

Abstract

This paper looks at Cayley map embeddings of complete graphs on orientable surfaces. Cayley maps constrain graph embeddings to those with cyclical edge rotations, so optimal embeddings on surfaces with the minimum genus may not always be possible. We explore instances when Cayley maps succeed at optimally embedding complete graphs, and when optimal embeddings are not possible, we determine how close to optimal they can get by finding vertex rotations that result in the smallest possible genus. Many of the complete graphs we consider have prime numbers of vertices, so for each complete graph Kn we focus on mappings with the finite cyclic group Zn.

Comments

Additional Committee Member: Kevin Griffin

Rights Holder

Miriam Scheinblum

Available for download on Wednesday, May 04, 2022

Share

COinS