Abstract
Let \(G=(V,A)\) be a directed graph, and let \(S\subseteq V\) be a set of vertices. Let the sequence \(S=S_0\subseteq S_1\subseteq S_2\subseteq \cdots \) be defined as follows: \(S_1\) is obtained from \(S_0\) by adding all out-neighbors of vertices in \(S_0\). For \(k\geqslant 2\), \(S_k\) is obtained from \(S_{k-1}\) by adding all vertices w such that for some vertex \(v\in S_{k-1}\), w is the unique out-neighbor of v in \(V\setminus S_{k-1}\). We set \(M(S)=S_0\cup S_1\cup \cdots \), and call S a power dominating set for G if \(M(S)=V(G)\). The minimum cardinality of such a set is called the power domination number of G. In this paper, we determine the power domination numbers of de Bruijn and Kautz digraphs.
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The authors would like to thank Dr. Joe Ryan for his valuable comments and suggestions to improve the quality of the paper.
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Grigorious, C., Kalinowski, T., Stephen, S. (2018). On the Power Domination Number of de Bruijn and Kautz Digraphs. In: Brankovic, L., Ryan, J., Smyth, W. (eds) Combinatorial Algorithms. IWOCA 2017. Lecture Notes in Computer Science(), vol 10765. Springer, Cham. https://doi.org/10.1007/978-3-319-78825-8_22
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