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In this paper, an adaptive minimum spanning tree based topology control algorithm for mobile ad-hoc networks (MANETs) is presented. Logically, mobile nodes know their source, destination and trajectory. Therefore, every node can inform the nodes around it about its trajectory. Equipped with this knowledge, the node will then be able to compute the relocations of its neighbours and determines the time points at which it must adjust its transmission radius. At each time point, node u establishes a minimum spanning tree and considers the nodes which are its neighbours in the tree as its neighbours in the final topology. In contrast to the existing algorithms, we analytically prove that at each time point of network lifespan, connectivity is preserved. The algorithm can proactively adapt the network changes without relying on periodic beacons. In addition, message overhead is put to the network locally and occurs only if the nodes change their trajectories or lose/discover a neighbour(s). Simulation experiments are conducted to measure performance benefits with reference to three metrics, namely: node degree, transmission radius, packet loss ratio.