On the power domination number of the generalized Petersen graphs

Guangjun Xu () and Liying Kang
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Guangjun Xu: The University of Melbourne
Liying Kang: Shanghai University

Journal of Combinatorial Optimization, 2011, vol. 22, issue 2, No 11, 282-291

Abstract: 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.

Keywords: Power domination number; The generalized Petersen graph (search for similar items in EconPapers)
Date: 2011
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Citations: View citations in EconPapers (4)

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DOI: 10.1007/s10878-010-9293-y

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