Commun. Math. Res., 32 (2016), pp. 332-338.
Published online: 2021-05
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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 $D$.
}, issn = {2707-8523}, doi = {https://doi.org/10.13447/j.1674-5647.2016.04.05}, url = {http://global-sci.org/intro/article_detail/cmr/18905.html} }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 $D$.