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.
Recommended Citation
Scheinblum, Miriam, "Cayley Map Embeddings of Complete Graphs" (2021). Honors Program Theses. 151.
https://scholarship.rollins.edu/honors/151
Rights Holder
Miriam Scheinblum
Included in
Algebra Commons, Discrete Mathematics and Combinatorics Commons, Geometry and Topology Commons
Comments
Additional Committee Member: Kevin Griffin