Total domination dot-stable graphs

Citations of this article
Mendeley users who have this article in their library.


A set S of vertices in a graph G is a total dominating set if every vertex of G is adjacent to some vertex in S. The minimum cardinality of a total dominating set of G is the total domination number of G. Two vertices of G are said to be dotted (identified) if they are combined to form one vertex whose open neighborhood is the union of their neighborhoods minus themselves. We note that dotting any pair of vertices cannot increase the total domination number. Further we show it can decrease the total domination number by at most 2. A graph is total domination dot-stable if dotting any pair of adjacent vertices leaves the total domination number unchanged. We characterize the total domination dot-stable graphs and give a sharp upper bound on their total domination number. We also characterize the graphs attaining this bound. © 2011 Elsevier B.V. All rights reserved.




Rickett, S. A., & Haynes, T. W. (2011). Total domination dot-stable graphs. Discrete Applied Mathematics, 159(10), 1053–1057.

Register to see more suggestions

Mendeley helps you to discover research relevant for your work.

Already have an account?

Save time finding and organizing research with Mendeley

Sign up for free