Abstract
Monitoring an electric power system with a minimum number of PMUs is related to the domination problem in graph theory. In this paper, we introduce a new graph invariant called global power domination number. A power dominating set S of a graph G = (V, E) is a global power dominating set if S is also a power dominating set of . The global power domination number γgp (G) is the minimum cardinality of a global power dominating set. In this paper, we initiate the study of global power domination problem and prove its NP-completeness. We also characterize the global power domination number for trees and compute the exact value of γgp (G) for certain families of graph.
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