The Twin Domination Number of Strong Product of Digraphs

Abstract

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 the twin 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 product of two digraphs, and prove that the twin domination number of strong product of the complete digraph and any digraph $D$ equals the twin domination number of $D$.