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.
","abstract_html":"<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>","abstract_has_math":false,"creators":["Collins, Alexander Raymond"],"institution":null,"degree_name":"Master of Science in Mathematics (M.S.)","degree_level":"Thesis (restricted to Georgia Southern)","degree_discipline":"Department of Mathematical Sciences","degree_department":null,"school":null,"contributors":["Alina Iacob","Emil Iacob","Colton Magnant"],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2012,"date_issued":"2012-01-01T08:00:00Z","date_published":"2012-01-01T08:00:00Z","updated_at":"2026-07-24T02:27:19Z","subjects":["ETD","Pure mathematics","Mathematics","Graph theory","Applied mathematics","Algebra","Mathematical modeling"],"languages":[],"rights":[],"rights_urls":[],"identifier_entries":[]},"links":{"outbound_url":"https://digitalcommons.georgiasouthern.edu/etd/679","outbound_label":"Repository record","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor","label":"Contributor","values":["Alina Iacob","Emil Iacob","Colton Magnant"]},{"key":"dc:creator","label":"Author","values":["Collins, Alexander Raymond"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date.available","label":"Dc Date Available","values":["2013-08-07T07:00:00Z"]},{"key":"thesis:degree_discipline","label":"Discipline","values":["Department of Mathematical Sciences"]},{"key":"thesis:degree_level","label":"Degree Level","values":["Thesis (restricted to Georgia Southern)"]},{"key":"thesis:degree_name","label":"Degree Name","values":["Master of Science in Mathematics (M.S.)"]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["ETD","Pure mathematics","Mathematics","Graph theory","Applied mathematics","Algebra","Mathematical modeling"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["https://digitalcommons.georgiasouthern.edu/etd/679"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description.abstract","label":"Abstract","values":["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.
"]},{"key":"dc:title","label":"Title","values":["Geometric and Algebraic Graphs and their Applications"]}]}],"canonical_facts":{"dc:contributor":["Alina Iacob","Emil Iacob","Colton Magnant"],"dc:creator":["Collins, Alexander Raymond"],"dc:date.available":["2013-08-07T07:00:00Z"],"dc:description.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.
"],"dc:identifier":["https://digitalcommons.georgiasouthern.edu/etd/679"],"dc:subject":["ETD","Pure mathematics","Mathematics","Graph theory","Applied mathematics","Algebra","Mathematical modeling"],"dc:title":["Geometric and Algebraic Graphs and their Applications"],"thesis:degree_discipline":["Department of Mathematical Sciences"],"thesis:degree_level":["Thesis (restricted to Georgia Southern)"],"thesis:degree_name":["Master of Science in Mathematics (M.S.)"]},"updated_at":"2026-07-24T02:27:19Z"}