The oscillation of neutrino flavors, due to its interferometry nature, is extremely sensitive to the phase differences developing during the propagation of neutrinos. In this paper we investigate the effect of the Violation of Equivalence Principle (VEP) on the flavor oscillation probabilities of atmospheric and cosmic neutrinos observed at neutrino telescopes such as IceCube. Assuming a general parameterization of VEP, dubbed extended parameter space, we show that the synergy between the collected data of high energy atmospheric and cosmic neutrinos severely constrains the VEP parameters. Also, the projected sensitivity of IceCube-Gen2 to VEP parameters is discussed.
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