Geometric and Algebraic Graphs and their Applications

<p>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.</p>

Name thesis:degree_name

Master of Science in Mathematics (M.S.)

Level thesis:degree_level

Thesis (restricted to Georgia Southern)

Discipline thesis:degree_discipline

Department of Mathematical Sciences

Year dc:date.available

2012

Author dc:creator

• Collins, Alexander Raymond

Contributors dc:contributor

• Alina Iacob
• Emil Iacob
• Colton Magnant

• ETD
• Pure mathematics
• Mathematics
• Graph theory
• Applied mathematics
• Algebra
• Mathematical modeling

Repository record dc:identifier

https://digitalcommons.georgiasouthern.edu/etd/679

OAI identifier oai:identifier

oai:digitalcommons.georgiasouthern.edu:etd-1679