We investigate the reflectionlessness and invisibility properties of the transverse electric-mode solution of a linear homogeneous optical system which comprises PT-symmetric structures covered by graphene sheets. We derive analytic expressions, indicate the roles of each parameter governing the optical system with graphene, and prove that optimal conditions of these parameters give rise to broadband and wide-angle invisibility. The presence of graphene turns out to shift the invisible wavelength range and to reduce the required gain value considerably, based on its chemical potential and temperature. We substantiate that our results yield broadband reflectionless and invisible configurations for realistic materials of small refractive indices, usually around eta = 1, and of small thicknesses with graphene sheets of rather low temperatures and chemical potentials. Finally, we demonstrate that pure PT-symmetric graphene yields invisibility at low temperatures and chemical potentials.