In this paper, we propose new core nodes based stable ad-hoc routing scheme using synchronizations, as a critical factor of optimal routing path selection and its management, for stable and robust routing in large-scale wireless mobile ad-hoc networks. First, we proposed an ad-hoc network model including the concepts of hub and bridge node, spatial, time and mobility synchronization. Next, we proposed optimal core nodes based stable routing protocols using these network models. For the optimal core routing path selection, we derived a mathematical formulation using reconstructed core network topology. The performance of the proposed routing algorithm is evaluated in comparison with legacy ad-hoc routing algorithms such as DSR and CBRP with respect to average throughput, average normalized control overhead and average end-to-end delay jitter. The performance evaluation results show that our routing protocol has better performance than DSR and CBRP in large scale ad hoc networks.