The Twin Domination Numb er of Strong Pro duct of Digraphs

Let $γ^∗(D)$ denote the twin domination number of digraph $D$ and let $D_1 ⊗ D_2$ denote the strong product of $D_1$ and $D_2$. In this paper, we obtain that thetwin domination number of strong product of two directed cycles of length at least $2$.Furthermore, we give a lower bound of the twin domination number of strong productof two digraphs, and prove that the twin domination number of strong product of thecomplete digraph and any digraph $D$ equals the twin domination number of $D$.