On the power domination number of the generalized Petersen graphs |
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Authors: | Guangjun Xu Liying Kang |
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Affiliation: | 1.Department of Mathematics and Statistics,The University of Melbourne,Parkville,Australia;2.Department of Mathematics,Shanghai University,Shanghai,China |
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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 γ 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. |
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