domination number; domatic number; total domination number; total domatic number; restrained domination number; restrained domatic number; total restrained domination number; total restrained domatic number
The restrained domination number $\gamma ^r (G)$ and the total restrained domination number $\gamma ^r_t (G)$ of a graph $G$ were introduced recently by various authors as certain variants of the domination number $\gamma (G)$ of $(G)$. A well-known numerical invariant of a graph is the domatic number $d (G)$ which is in a certain way related (and may be called dual) to $\gamma (G)$. The paper tries to define analogous concepts also for the restrained domination and the total restrained domination and discusses the sense of such new definitions.
 T. W. Haynes, S. T. Hedetniemi and P. J. Slater: Fundamentals of Domination in Graphs
. Marcel Dekker Inc., New York-Basel-Hong Kong, 1998. MR 1605684
 M. A. Henning: Graphs with large restrained domination number
. Discrete Math. 197/198 (1999), 415–429. MR 1674878
| Zbl 0932.05070