Domination in a digraph and in its reverse

Let D be a digraph. By @c(D) we denote the domintaion number of D and by D^- we denote a digraph obtained by reversing all the arcs of D. In this paper we prove that for every @d>=3 and k>=1 there exists a simple strongly connected @d-regular digraph D"@d","k such that @c(D"@d","k^-)-@c(D"@d","k)=k. Analogous theorem is obtained for total domination number provided that @d>=4.