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- W3003924041 abstract "Let $G = (V,E)$ be a simple, undirected and connected graph. A connected (total) dominating set $S subseteq V$ is a secure connected (total) dominating set of $G$, if for each $ u in V setminus S$, there exists $v in S$ such that $uv in E$ and $(S setminus lbrace v rbrace) cup lbrace u rbrace $ is a connected (total) dominating set of $G$. The minimum cardinality of a secure connected (total) dominating set of $G$ denoted by $ gamma_{sc} (G) (gamma_{st}(G))$, is called the secure connected (total) domination number of $G$. In this paper, we show that the decision problems corresponding to secure connected domination number and secure total domination number are NP-complete even when restricted to split graphs or bipartite graphs. The NP-complete reductions also show that these problems are w[2]-hard. We also prove that the secure connected domination problem is linear time solvable in block graphs and threshold graphs." @default.
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- W3003924041 date "2020-02-03" @default.
- W3003924041 modified "2023-10-16" @default.
- W3003924041 title "Algorithmic Complexity of Secure Connected Domination in Graphs" @default.
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- W3003924041 doi "https://doi.org/10.48550/arxiv.2002.00713" @default.
- W3003924041 hasPublicationYear "2020" @default.
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