On the $$p$$ -reinforcement and the complexity

You Lu (), Fu-Tao Hu () and Jun-Ming Xu ()
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You Lu: Northwestern Polytechnical University
Fu-Tao Hu: University of Science and Technology of China
Jun-Ming Xu: University of Science and Technology of China

Journal of Combinatorial Optimization, 2015, vol. 29, issue 2, No 4, 389-405

Abstract: Abstract Let $$G=(V,E)$$ be a graph and $$p$$ be a positive integer. A subset $$S\subseteq V$$ is called a $$p$$ -dominating set if each vertex not in $$S$$ has at least $$p$$ neighbors in $$S$$ . The $$p$$ -domination number $$\gamma _p(G)$$ is the size of a smallest $$p$$ -dominating set of $$G$$ . The $$p$$ -reinforcement number $$r_p(G)$$ is the smallest number of edges whose addition to $$G$$ results in a graph $$G^{\prime }$$ with $$\gamma _p(G^{\prime })

Keywords: Domination; $$p$$ -Domination; $$p$$ -Reinforcement; NP-hard (search for similar items in EconPapers)
Date: 2015
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DOI: 10.1007/s10878-013-9597-9

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