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An implementation of plasmon-induced transparency (PIT) composed of a bus waveguide coupled to a rectangular nanocavity and an H-shape resonator is studied. It is shown that the wavelength, transmission, and width of the PIT peak can be tuned by adjusting the geometrical parameters of the H-resonator, such as the gap between the resonators, width, and position of the middle slit among the branches. For avoiding oxidization of the structure, the effect of coating a thin graphene layer on the inner walls of the H-resonator is investigated. It is shown that the proposed structure can be used as a nanosensor with a refractive index sensitivity of 1300 nm. and figure of merit equal to and also as a compact nanoswitch with transmission 76% and a modulation depth equal to 19.77 dB.