Research studies show that energy consumption in communication networks is mainly related to active network elements such as communication links. Based on this approach, several energy management techniques, generally known as green techniques, have been proposed. Their main goal is to minimize energy consumption by routing network traffic through a set of network resources and powering off the remaining unused resources. However, this approach imposes a signaling overhead on the routing system due to selectively powering off/on the network resources. In this work, we investigate the trade-off between energy efficiency and signaling overhead in a software defined network (SDN) domain with a single controller. To this end, we formulate an integer linear programming (ILP) problem whose objective function is to minimize the control overhead by taking into account the total energy consumption of the network. We then propose two polynomial-time heuristic algorithms to find near-optimal solutions for the problem. We evaluate the performance of our heuristic algorithms by comparison with the results obtained from our ILP formulation using optimization software CPLEX.