The product of the restrained domination numbers of a graph and its complement.

Let G = ( V,E) be a graph. A set S ⊆ V is a restrained dominating set if every vertex in V − S is adjacent to a vertex in S and to a vertex in V − S. The restrained domination number of G, denoted γ( G), is the smallest cardinality of a restrained dominating set of G. In this paper, we show that if G is a graph of order n ≥ 4, then $$\gamma _r \left( G \right)\gamma _r \left( {\bar G} \right) \leqslant 2n$$. We also characterize the graphs achieving the upper bound. [ABSTRACT FROM AUTHOR]