Degree Name

MS (Master of Science)


Mathematical Sciences

Date of Award


Committee Chair or Co-Chairs

Teresa W. Haynes

Committee Members

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.

Document Type

Thesis - unrestricted


Copyright by the authors.