Geodesic
Remarks on restrained domination and total restrained domination in graphs
Czechoslovak Mathematical Journal, Tome 55 (2005) no. 2, pp. 393-396
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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.
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.
Classification : 05C35, 05C69
Keywords: domination number; domatic number; total domination number; total domatic number; restrained domination number; restrained domatic number; total restrained domination number; total restrained domatic number 
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Zelinka, Bohdan. Remarks on restrained domination and total restrained domination in graphs. Czechoslovak Mathematical Journal, Tome 55 (2005) no. 2, pp. 393-396. http://geodesic.mathdoc.fr/item/CMJ_2005_55_2_a8/

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