In this work, a new technique for the computation of the region of attraction for linear and time invariant systems controlled by a saturated reset control system is presented. The estimation of the region of attraction is based on a polytopic representation. In addition, the information of the solutions is synthesized in a directed graph formed by the polytopes. After presenting several useful conditions on the polytopes, such as positive invariance and convergence to the origin, a procedure is proposed to process the graph and obtain a region of attraction estimation. The effectiveness of the proposed technique is illustrated by a numerical example.