This paper introduces the problem of fault tolerant topology control for one-to-all communications in symmetric wireless networks. We investigate two algorithms to address the problem, namely Minimum Weight Based Algorithm (MWBA) and Nearest Neighbor Augmentation Algorithm (NNAA), and prove that the former is a 4k approximation and the latter is a (k + 4) approximation. Through simulations, we evaluate the average performance of these two algorithms and find that MWBA is slightly better than NNAA in terms of the total power consumption.