Although green networking and fairness are both vital and rapidly increasing areas of research, providing energy-fairness in multi-domain green networks is a hitherto unexplored issue. In this study, the authors address energy-fair routing in multi-domain green networks by formulating an optimisation problem as an integer linear programme. The authors' problem maximises the energy saving of the domain with minimum energy saving while ensuring that the energy consumption of each domain is below a given threshold. The model they have established in this study also provides a flexible bandwidth assignment mechanism which improves the feasibility performance of their methods. They then propose a polynomial-time heuristic algorithm for this problem. They evaluate the performance of their heuristic algorithm by comparison with the results obtained from their integer linear programming formulation using optimisation software CPLEX. The simulation results demonstrate that the heuristic algorithm yields close results to the values obtained from the CPLEX implementation of their proposed formulation in terms of energy-fairness and outperforms the previous results while at the same time having low computational complexity.