Complete Bipartite Graph Embeddings on Orientable Surfaces Using Cayley Maps

Author

Madeline SpiesFollow

Date of Award

Spring 2020

Thesis Type

Open Access

Degree Name

Honors Bachelor of Arts

Department

Mathematics

Sponsor

Dr. Mark Anderson

Committee Member

Dr. Jay Yellen

Committee Member

Dr. Whitney Coyle

Abstract

We explored how effective Cayley Maps are at embedding complete bipartite graphs onto orientable surfaces, such as spheres and tori. We embedded the graphs onto surfaces using Cayley Maps with the intent of finding rotations that result in the graphs’ optimal genera. Because there are only three groups that can be used to describe Kp,p, where p is prime, we chose to focus on this specific graph type. This paper explains how we determined the genera when using a Cayley Map, provides general theorems for surface face sizes and the Dihedral Group, and discusses our results for Kp,p up to p=11.

Comments

Dr. Sheri Boyd was also a Committee Member.

Recommended Citation

Spies, Madeline, "Complete Bipartite Graph Embeddings on Orientable Surfaces Using Cayley Maps" (2020). Honors Program Theses. 116.
https://scholarship.rollins.edu/honors/116

Rights Holder

Madeline Spies