Reachability is among the most common problems to address when working on graphs since it is the base for many other algorithms, and scalable solutions have become of paramount importance with the advent of distributed systems that process large amounts of data. Specifically many applications explore graphs with millions of nodes and vertices, which explains why the development of fast and scalable algorithms entails complex challenges. Modern GPUs are highly parallel systems based on many-core architectures and have gained popularity in parallelizing algorithms that run on large data sets. In this context the NVIDIA CUDA platform has been used to provide a concrete implementation of the developed algorithms.