On the power domination number of the generalized Petersen graphs

Authors:
Guangjun Xu;Liying Kang
Affiliations:
Department of Mathematics and Statistics, The University of Melbourne, Parkville, Australia 3010;Department of Mathematics, Shanghai University, Shanghai, China 200444
Venue:
Journal of Combinatorial Optimization
Year:
2011

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Abstract

The problem of monitoring an electric power system by placing as few measurement devices in the system as possible is closely related to the well-known domination problem in graphs. Following a set of rules for power system monitoring, a set S of vertices is defined to be a power dominating set of a graph if every vertex and every edge in the system is monitored by the set S. The minimum cardinality of a power dominating set of G is the power domination number 驴 p (G). In this paper, we investigate the power domination number for the generalized Petersen graphs, presenting both upper bounds for such graphs and exact results for a subfamily of generalized Petersen graphs.