Geodesic
Power Domination in the Generalized Petersen Graphs
Discussiones Mathematicae. Graph Theory, Tome 40 (2020) no. 3, pp. 695-712

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The problem of monitoring an electric power system by placing as few measurement devices in the system can be formulated as a power dominating set problem in graph theory. The power domination number of a graph is the minimum cardinality of a power dominating set. Xu and Kang [On the power domination number of the generalized Petersen graphs, J. Comb. Optim. 22 (2011) 282–291] study the exact power domination number for the generalized Petersen graph P (3k, k), and propose the following problem: determine the power domination number for the generalized Petersen graph P (4k, k) or P (ck, k). In this paper we give the power domination number for P (4k, k) and present a sharp upper bound on the power domination number for the generalized Petersen graph P (ck, k).
Keywords: power domination, domination, generalized Petersen graph, electric power system 
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Zhao, Min; Shan, Erfang; Kang, Liying. Power Domination in the Generalized Petersen Graphs. Discussiones Mathematicae. Graph Theory, Tome 40 (2020) no. 3, pp. 695-712. http://geodesic.mathdoc.fr/item/DMGT_2020_40_3_a0/