Date of Award

12-2016

Level of Access Assigned by Author

Open-Access Thesis

Degree Name

Master of Arts (MA)

Department

Mathematics

Advisor

Robert Franzosa

Second Committee Member

Andrew Knightly

Third Committee Member

Benjamin Weiss

Abstract

The purpose of this thesis is to study hypercube graphs and their embeddings on orientable surfaces. We use rotation systems to represent these embeddings. We prove some results about the effect of adjacent switches in rotation system and create a rotation system called the ABC rotation system and prove general results about it. Using this rotation system, we give a general theorem about the minimal embedding of $Q_{n}$. We also look at some interesting types of maximal embedding of $Q_{n}$, such as the Eulerian walk embedding and the "big-face embedding". We prove a theorem that gives a recursively constructive way of obtaining the latter embedding in $Q_{n}$

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