Bounds on several versions of restrained domination number
Keywords:restrained domination, restrained double domination, total restrained domination
AbstractWe investigate several versions of restrained
domination numbers and present new bounds on these parameters. We generalize the
concept of restrained domination and improve some well-known bounds in the literature.
In particular, for a graph $G$ of order $n$ and minimum degree $\delta\geq 3$, we prove that
the restrained double domination number of $G$ is at most $n-\delta+1$. In addition,
for a connected cubic graph $G$ of order $n$ we show that
the total restrained domination number of $G$ is at least $n/3$ and
the restrained double domination number of $G$ is at least $n/2$.
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