Term of Award

Spring 2012

Degree Name

Master of Science in Mathematics (M.S.)

Document Type and Release Option

Thesis (restricted to Georgia Southern)

Department

Department of Mathematical Sciences

Committee Chair

Wang, Hua

Committee Member 1

Alina Iacob

Committee Member 2

Emil Iacob

Committee Member 3

Colton Magnant

Committee Member 3 Email

cmagnant@georgiasouthern.edu

Abstract

In this thesis, we begin with a look at the Wiener Index and its correlation with the boiling point of a hydrocarbon. Though the Wiener Index correlates physical properties of chemical compounds relatively well, we produce a new method of modeling the hydrocarbons and their chemical property which creates a geometric graph that we can analyze. Then we take a look at a classic conjecture colloquially known as "The Middle Two Levels Conjecture." This problem in pure graph theory involves finding Hamiltonian cycles in a power set on n elements. We take advantage of the fact that it is an algebraic graph to produce a method of finding large cycles in the graph. Finally we investigate a method of finding Super Edge-graceful labeling (SEGL) on graphs. We make an effort to generate infinite families that have a SEGL and continue research to be able to classify graphs into categories of those with a SEGL and those without.

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