Recently, deep learning has emerged as a promising approach for solving challenging resource distribution (RD) problems in vehicle-to-everything (V2X) wireless networks. How-ever, existing neural network architectures lack scalability, in-terpretability, and generalization. To address these limitations, in this study, we propose a new flexible graph neural network (FGNN)-based resource distribution framework for vehicle-to-vehicle (V2V) and vehicle-to-infrastructure (V2I) user selection and power management in V2X networks with several next- generation access points (APs) and a cluster of V2V and V2I communication users. In the proposed framework, we formu-lated an optimization problem with each V2V and V2I user with the least power constraint that adapts to V2X wireless network settings through training inactive users. Likewise, we consider the situation when every V2I user shares the band with a different group of V2V users. Moreover, we introduce a parameterization of the RD framework strategy employing a flexible graph neural network (FGNN) context derived from instantaneous channel conditions to learn the low-dimension features of every user/vehicle. To assess the execution of the framework, we conduct simulation experiments comparing it with baseline methods in terms of efficiency, sum rate, and fairness.