Date of Award
Honors Bachelor of Arts
Dr. Mark Anderson
Dr. Jay Yellen
Dr. Sheri Boyd
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.
Scheinblum, Miriam, "Cayley Map Embeddings of Complete Graphs" (2021). Honors Program Theses. 151.
Available for download on Wednesday, May 04, 2022