Journal of Combinatorial Optimization

, Volume 22, Issue 2, pp 282–291 | Cite as

On the power domination number of the generalized Petersen graphs

  • Guangjun Xu
  • Liying Kang


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.


Power domination number The generalized Petersen graph 


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Copyright information

© Springer Science+Business Media, LLC 2010

Authors and Affiliations

  1. 1.Department of Mathematics and StatisticsThe University of MelbourneParkvilleAustralia
  2. 2.Department of MathematicsShanghai UniversityShanghaiChina

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