This study introduces an innovative framework for addressing the maximum independent set (MIS) and minimum vertex cover (MVC) problems using a graph neural network (GNN) approach inspired by dynamic programming (DP). The MIS problem finds important applications in Communication Networks, as it can help in optimizing the network's performance by ensuring non-interfering or non-conflicting communication between nodes. Instead, identifying an MVC in a network helps to minimize the number of resources needed for infrastructure deployment, which is crucial in applications like transportation or utility networks. Unfortunately, the MIS and MVC are NP-hard problems, and classic heuristics, like the simplex or the ellipsoid methods, may take too much time to find a solution.