Counterpart of dominating sets in graphs

A $$t$$-fold dominating set in a simple undirected graph $$G$$ with vertex set $$V$$ is a subset $$D\subseteq V$$ such that each vertex of $$V\setminus D$$ has at least $$t$$ neighbours in $$D$$.

I am interested in the counterpart: a (proper) subset $$M\subset V$$ such that each vertex not in $$M$$ has at most $$t$$ neighbours in $$M$$. Is there a name for such subsets? If there is, could you please give me some references to papers dealing with this type of questions?

I am studying such sets in order to produce subgraphs of a graph with high minimal degree.

I only know that if $$D\subset V$$ has the property that each vertex not in $$D$$ has exactly $$t$$ neighbours in $$D$$ are called $$t$$-fold perfect dominating sets. (Leastwise for $$t=1$$, it is quite common to call them perfect dominating sets.)

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