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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机译：通过在系统中放置尽可能少的测量设备来监视电力系统的问题与众所周知的图形控制问题密切相关。遵循一组用于电力系统监控的规则，如果系统S中的每个顶点和每个边都由集合S监控，则将顶点集S定义为图的功率控制集。功率控制集的最小基数G的代表功率控制数γ p （G）。在本文中，我们研究了广义Petersen图的幂控制数，同时给出了此类图的上限和广义Petersen图的一个子族的精确结果。
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