Discrete Mathematics and Combinatorics Commons^™

Cayley Map Embeddings Of Complete Graphs With Even Order, Michael O'Connor

Honors Program Theses

German mathematician Claus Michael Ringel used voltage graphs to embed complete graphs onto orientable surfaces such that none of the graph's edges cross each other. Cayley maps do the same whilst being simpler to work with. The goal is to determine the efficiency of Cayley maps in embedding complete graphs onto orientable surfaces. This article focus on complete graphs of even order with an emphasis on graphs whose orders are congruent to 6 modulo 12 and 0 modulo 12. We establish 12 distinct classes that each have their own unique qualities. Through the generalization of a previous technique, we prove …