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In this paper, physical models are derived for the effective resistance of multilayer graphene nanoribbon (m-GNR) interconnects. The impact of finite resistive coupling between the layers for top contacted m-GNR interconnects is considered. It is found that the addition of more parallel layers does not necessarily translate into a decrease in the overall resistance of m-GNR interconnects. Rather, the improvement in the effective resistance saturates with an increase in the number of layers. The optimal number of layers to minimize the delay and the energy-delay product of m-GNR interconnects is also evaluated. It is found that the optimal number of layers is a function of the interconnect length, interlayer resistance, and the kind of contact that is used. It is demonstrated that, for short interconnect lengths, m-GNR interconnects with smooth edges perform better compared to copper wires.