MS (Master of Science)
Date of Award
Committee Chair or Co-Chairs
Teresa W. Haynes
Debra J. Knisley, Anant P. Godbole
Two vertices are said to be identifed if they are combined to form one vertex whose neighborhood is the union of their neighborhoods. A graph is total domination dot-critical if identifying any pair of adjacent vertices decreases the total domination number. On the other hand, a graph is total domination dot-stable if identifying any pair of adjacent vertices leaves the total domination number unchanged. Identifying any pair of vertices cannot increase the total domination number. Further we show it can decrease the total domination number by at most two. Among other results, we characterize total domination dot-critical trees with total domination number three and all total domination dot-stable graphs.
Thesis - Open Access
McMahon, Stephanie Anne Marie, "Total Domination Dot Critical and Dot Stable Graphs." (2010). Electronic Theses and Dissertations. Paper 1687. https://dc.etsu.edu/etd/1687
Copyright by the authors.