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Existing solutions only focus on the utility of coverage or energy efficient coverage by considering target connectivity for battery-powered WSNs. This paper focuses on optimizing the maximum monitoring frequency with guaranteed target coverage and connectivity in EH-WSNs. We first analyzed the factors affecting monitoring quality and the energy harvesting model. Thereafter, we presented the problem formulation and proposed the algorithm for maximizing monitoring frequency and guaranteeing target coverage and connectivity (MFTCC) that is based on graph theory. Furthermore, we presented the corresponding distributed implementation approach. On the basis of the existing energy harvesting prediction model, expensive simulations show that the proposed MFTCC algorithm achieves high average maximum monitoring frequency and energy usage ratio. 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