Power conservation is a critical issue for ad hoc wireless networks. The main objective of the paper is to find the minimum uniform transmission power of an ad hoc wireless network, where each node uses the same transmission power, while maintaining network connectivity. Three different algorithms, binary search, Prim?s MST and its extension are developed to solve the problem, and their performance is compared by simulation study together with Kruskal?s minimum spanning tree (MST), a known solution proposed by Ramanathan and Rosales-Hain for topology control by transmission power adjustment. Our results show that Prim?s MST outperforms both Kruskal?s MST and binary search. The performance between Prim?s MST implemented with binary heap and Fibonacci heap is fairly close.