Abstract
Power utilities must track their power networks to respond to changing demand and availability conditions to ensure effective and efficient operation. As a result, several power companies employ phase measuring units (PMUs) to check their power networks continuously. Supervising an electric power system with the fewest possible measurement equipment is precisely the vertex covering graph-theoretic problem, in which a set D 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 γp(G) is the minimal cardinality of a PDS of a graph G. In this present study, the PDS is identified for octahedral networks.
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