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- W2560242983 abstract "Let $G=(V,E)$ be a graph, $k$ is a positive integer and let $S=(U,X)$ be a semigraph. A subset $Dsubseteq V$ is called a $k-$strong(weak) dominating set of the graph $G$ if every vertex $vin V-D$ is strongly(weakly) dominated by at least $k$ vertices of $D$. The $k-$strong(weak)domination number $gamma_k^s ~(gamma_k^w)$ is the minimum cardinality of $k-$strong(weak) dominating set of $G$. A subset $D subseteq U$ is called $k-$ strong(weak) adjacent dominating set of semigraph $S$ if every vertex $uin U-D$ is strongly(weakly) adjacent dominated by at least $k$ vertices of $D$. The minimum cardinality of a $k-$ strong adjacent dominating set, a $k-$ weak adjacent dominating set are respectively denoted as $gamma_k^{s,a}(S)$ and $gamma_k^{w,a}(S)$. In this paper, we determine $gamma_k^s $ and $gamma_k^w $ for standard graphs. Also, we establish bounds on the above domination parameters for graphs and semigraphs. We prove that the $k-$strong(weak) domination problem is NP-complete for general graphs." @default.
- W2560242983 created "2016-12-16" @default.
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- W2560242983 date "2016-11-30" @default.
- W2560242983 modified "2023-09-23" @default.
- W2560242983 title "k−strong k−weak domination in graphs and semigraphs" @default.
- W2560242983 hasPublicationYear "2016" @default.
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