Besides the conventional spectral efficiency metric, energy efficiency (EE) has been adopted as one of the new mandatory performance metrics for green future mobile networks. In this sense, in this article we study energy-efficient radio resource allocation for dual-hop orthogonal frequency division multiple access relay networks considering multiple relays and users. Resource allocation in our scenario is comprised of relay selection, subcarrier pairing, subcarrier assignment, and transmit power allocation. Particularly, in the context of EE with quality of service constraints, three different problems, namely, power consumption minimization, global EE maximization, and minimum individual EE maximization are addressed. For tackling them, first, we demonstrate a property that exploits the use of the decode and forward protocol employed in the relays and we show how it can be applied to simplify the investigated problems. Although some of these problems are nonconvex due to the fractional objective functions and integer optimization domain, optimal solutions are provided using generalized fractional programming theory to transform the fractional objective functions to the subtractive forms. Then, by employing Dinkelbach or bisection methods, we propose iterative algorithms where a parametric problem is solved in each iteration until reaching convergence. By introducing a penalty function to handle integer variables and applying majorization-minimization approach, we make the parametric problem convex and we propose suboptimal iterative solutions with reduced computational cost. Regarding obtained simulation results, we discuss the performance of the involved solutions in terms of global EE and fairness with respect to different parameters of the system.