We investigate PT-symmetric coherent perfect absorbers (CPAs) in the TE mode solution of a linear homogeneous optical system surrounded by graphene sheets. It is revealed that the presence of graphene sheets plays a role to adjust the enhancement of absorption in a CPA. We derive exact analytic expressions and work through their possible impacts on lasing threshold and CPA conditions. We point out the roles of each parameter governing an optical system with graphene, and we show that optimal conditions of these parameters give rise to enhancement and possible experimental realization of a CPA laser. The presence of graphene leads the required gain amount to reduce considerably based on its chemical potential and temperature. We obtain that the relationship among system parameters decides the measure of CPA conditions. We find that graphene features that contribute to the resonance effect in graphene sheets are rather preferable to build a better CPA. (c) 2018 Optical Society of America.