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Supervising an electric power system with the fewest possible measurement equipment is precisely the vertex covering graph-theoretic problem, in which a set <jats:italic>D<\/jats:italic> is defined as a power dominating set (PDS) of a graph if it supervises every components (vertices and edges) in the system (with a couple of rules). The <jats:italic>\u03b3<\/jats:italic><jats:sub><jats:italic>p<\/jats:italic><\/jats:sub>(<jats:italic>G<\/jats:italic>) is the minimal cardinality of a PDS of a graph <jats:italic>G<\/jats:italic>. 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