Achieving energy efficiency has in recent times become a major concern of networking research due to the ever-escalating power consumption and CO2 emissions produced by large data networks. This problem is becoming more and more challenging because of the drastic traffic increase in the last few years and it is expected to be increased even more in the coming years. Using efficient energy-aware strategies that could overturn this situation by reducing the electricity consumption as well as mitigating the environmental impact of data transmission networks. However, CO2 and energy consumption cannot be considered proportionate if the means of electricity production differs. This research work focuses on reducing the environmental impact of data transmission network by implementing energy aware routing, where unused network devices will be put into sleep/shut down and high capacity links will be adapted according to demand requirement. But, alongside with energy, this work has introduced two different metrics namely carbon emission factor and non-renewable energy usage percentage, which are considered as objective functions for designing green network. Here a centralized approach like using Software-Defined Networking (SDN), is used for designing to solve this problem as they allow flexible programmability suitable for this problem. Our proposal proposes a routing technique using genetic algorithm that minimizes the number of network-elements required and at the same time adapt the bandwidth capacity while satisfying an incoming traffic load. Different from existing related works, we focus on optimizing not only energy consumption but also carbon emission and non-renewable energy consumption in SDN in order to close this important gap in the literature and provide solutions compatible with operational backbone networks. Complementing the general aim of improving the environmental impact of data transmission network, this research is also intended to cover important related features such as realistic large demand size, network performance, and Quality of Service (QoS) requirements. At the same time this work focuses on network stability and analyzes the impact of network stability while implementing a green solution. Our work proposes a penalty and filtering mechanism which helps to find an optimal balance between stability and green networking. By using realistic input data, significant values of switched-off links and nodes are reached which demonstrate the effectiveness of our algorithm. The obtained result validated the importance of considering environmental factors rather than considering only energy. Results also show the trade-off between environmental and performance concerns, considering a couple of performance indicators. Moreover, it is shown that the penalty and filtering mechanism is an effective approach to avoid incoherent system and improve the stability of the system. As a whole, this conducted research and contributions reported through this manuscript stand as a valuable solution on the road to sustainable networking.