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arXiv · 2002.00713

Algorithmic Complexity of Secure Connected Domination in Graphs

Jakkepalli Pavan Kumar·P. Venkata Subba Reddy·S. Arumugam
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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.

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Jakkepalli Pavan Kumar, P. Venkata Subba Reddy, S. Arumugam. 2020-02-03. Algorithmic Complexity of Secure Connected Domination in Graphs. https://arxiv.org/abs/2002.00713

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