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There are many trials to provide an optimal route for minimum energy consumption in a wireless sensor network. Currently, however, the mechanisms to find minimum energy property graph (MEPG) do not properly take into account the efficiency in time and storage, the optimality in results, and the feasibility in real systems. In this paper, we propose an efficient and first optimal algorithm to find the MEPG, in which all minimum energy paths are included, not only significantly reducing its total number of edges, but also obtaining an optimal result in O(VlogV+E). We also develop power aware data-centric routing protocol characterized by minimum energy consumption and longer lifetime.