Degree Name
MS (Master of Science)
Program
Mathematical Sciences
Date of Award
5-2000
Committee Chair or Co-Chairs
Teresa W. Haynes
Committee Members
Debra J. Knisley, James Boland
Abstract
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.
Document Type
Thesis - unrestricted
Recommended Citation
Dautermann, Robert Elmer III, "Vertices in Total Dominating Sets." (2000). Electronic Theses and Dissertations. Paper 5. https://dc.etsu.edu/etd/5
Copyright
Copyright by the authors.