Geodesic
$k$-domination on hexagonal cactus chains
Kragujevac Journal of Mathematics, Tome 36 (2012) no. 2, p. 335

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In this paper we use the concept of $k$-domination, where $k\geq 1$. We determine minimum $k$-dominating sets and $k$-domination numbers of three special types of hexagonal cactus chains. Those are para-, meta- and ortho-chains. For an arbitrary hexagonal chain $G_h$ of length $h\geq 1$ we establish the lower and the upper bound for $k$-domination number $\gamma_k$. As a consequence, we find the extremal chains due to $\gamma_k$.
Classification : 05C30
Keywords: $k$-dominating set, $k$-domination number, ortho-chain, para-chain, meta-chain. 
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Snježana Majstorović; Tomislav Došlić; Antoaneta Klobučar. $k$-domination on hexagonal cactus chains. Kragujevac Journal of Mathematics, Tome 36 (2012) no. 2, p. 335 . http://geodesic.mathdoc.fr/item/KJM_2012_36_2_a16/