Term of Award

Spring 2012

Degree Name

Master of Science in Mathematics (M.S.)

Document Type and Release Option

Thesis (restricted to Georgia Southern)

Copyright Statement / License for Reuse

Creative Commons License
This work is licensed under a Creative Commons Attribution 4.0 License.

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.

Research Data and Supplementary Material

No

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