Publication Date
Spring 2018
Advisor(s) - Committee Chair
Dominic Lanphier (Director), Tom Richmond, John Spraker, and Jason Rosenhouse
Degree Program
Department of Mathematics
Degree Type
Master of Science
Abstract
Hadwiger's conjecture is one of the deepest open questions in graph theory, and Cayley graphs are an applicable and useful subtopic of algebra.
Chapter 1 will introduce Hadwiger's conjecture and Cayley graphs, providing a summary of background information on those topics, and continuing by introducing our problem. Chapter 2 will provide necessary definitions. Chapter 3 will give a brief survey of background information and of the existing literature on Hadwiger's conjecture, Hamiltonicity, and the isoperimetric number; in this chapter we will explore what cases are already shown and what the most recent results are. Chapter 4 will give our decomposition theorem about PSL2 (R). Chapter 5 will continue with corollaries of the decomposition theorem, including showing that Hadwiger's conjecture holds for our Cayley graphs. Chapter 6 will finish with some interesting examples.
Disciplines
Algebra | Other Mathematics | Physical Sciences and Mathematics
Recommended Citation
Bell, Kathleen, "Cayley Graphs of PSL(2) over Finite Commutative Rings" (2018). Masters Theses & Specialist Projects. Paper 2102.
https://digitalcommons.wku.edu/theses/2102