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Volume 32, Issue 4
The Twin Domination Number of Strong Product of Digraphs

Hongxia Ma & Juan Liu

DOI: 10.13447/j.1674-5647.2016.04.05

Commun. Math. Res., 32 (2016), pp. 332-338.

Published online: 2021-05

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  • 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 $D$.

  • Keywords

twin domination number, strong product, directed cycle.

  • AMS Subject Headings

05C69, 05C76

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{CMR-32-332, author = {Ma , Hongxia and Liu , Juan}, title = {The Twin Domination Number of Strong Product of Digraphs}, journal = {Communications in Mathematical Research }, year = {2021}, volume = {32}, number = {4}, pages = {332--338}, 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 $D$.

}, 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} }
TY - JOUR T1 - The Twin Domination Number of Strong Product of Digraphs AU - Ma , Hongxia AU - Liu , Juan JO - Communications in Mathematical Research VL - 4 SP - 332 EP - 338 PY - 2021 DA - 2021/05 SN - 32 DO - http://doi.org/10.13447/j.1674-5647.2016.04.05 UR - https://global-sci.org/intro/article_detail/cmr/18905.html KW - twin domination number, strong product, directed cycle. AB -

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 $D$.

Ma , Hongxia and Liu , Juan. (2021). The Twin Domination Number of Strong Product of Digraphs. Communications in Mathematical Research . 32 (4). 332-338. doi:10.13447/j.1674-5647.2016.04.05
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