Abstract
dc:description.abstract<p>Fricke, Haynes, Hedetniemi, Hedetniemi, and Laskar introduced the following concept. For a graph <em>G</em> = (<em>V</em>,<em>E</em>), let <em>rho</em> denote a property of interest concerning sets of vertices. A vertex <em>u</em> is <em>rho-good</em> if <em>u</em> is contained in a {minimum, maximum} <em>rho-set</em> in <em>G</em> and <em>rho-bad</em> if <em>u</em> is not contained in a <em>rho-set</em>. Let <em>g</em> denote the number of <em>rho-good</em> vertices and <em>b</em> denote the number of <em>rho-bad</em> vertices. A graph <em>G</em> is called <em>rho-excellent</em> if every vertex in <em>V</em> is <em>rho</em>-good, <em>rho-commendable</em> if <em>g</em> > <em>b</em> > 0, <em>rho-fair</em> if <em>g</em> = <em>b</em>, and <em>rho-poor</em> if <em>g</em> < <em>b</em>. In this thesis the property of interest is total domination. The total domination number, <em>gamma<sub>t</sub></em>, is the cardinality of a smallest total dominating set in a graph. We investigate <em>gamma<sub>t</sub></em>-excellent, <em>gamma<sub>t</sub></em>-commendable, <em>gamma<sub>t</sub></em>-fair, and <em>gamma<sub>t</sub></em>-poor graphs.</p>
Degree
thesis:*- Name thesis:degree_name
- MS (Master of Science)
- Level thesis:degree_level
- Thesis - unrestricted
- Discipline thesis:degree_discipline
- Mathematical Sciences
- Year dc:date.issued
- 2000
Author and committee
dc:creator, dc:contributor.*- Author dc:creator
-
- Dautermann, Robert Elmer, III
Subjects
dc:subject × 5Rights
dc:rights- Statement dc:rights
-
- Copyright by the authors.
Identifiers
dc:identifier.*- Repository record dc:identifier
- https://dc.etsu.edu/etd/5
- OAI identifier oai:identifier
- oai:dc.etsu.edu:etd-1037