Remarks on restrained domination and total restrained domination in graphs

The restrained domination number γr(G) and the total restrained domination number γ tr(G) of a graph G were introduced recently by various authors as certain variants of the domination number γ(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 γ(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.