Fricke, Haynes, Hedetniemi, Hedetniemi, and Laskar introduced the following concept. For a graph G = (V,E), let rho denote a property of interest concerning sets of vertices. A vertex u is rho-good if u is contained in a {minimum, maximum} rho-set in G and rho-bad if u is not contained in a rho-set. Let g denote the number of rho-good vertices and b denote the number of rho-bad vertices. A graph G is called rho-excellent if every vertex in V is rho-good, rho-commendable if g > b > 0, rho-fair if g = b, and rho-poor if g < b. In this thesis the property of interest is total domination. The total domination number, gammat, is the cardinality of a smallest total dominating set in a graph. We investigate gammat-excellent, gammat-commendable, gammat-fair, and gammat-poor graphs.
| Identifer | oai:union.ndltd.org:ETSU/oai:dc.etsu.edu:etd-1037 |
| Date | 01 May 2000 |
| Creators | Dautermann, Robert Elmer, III |
| Publisher | Digital Commons @ East Tennessee State University |
| Source Sets | East Tennessee State University |
| Detected Language | English |
| Type | text |
| Format | application/pdf |
| Source | Electronic Theses and Dissertations |
| Rights | Copyright by the authors. |
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