Energy-saving is a critical issue in mobile computing. Given a set of hosts which forms a wireless ad hoc network and an initial energy for each host, this paper considers the topology control problem by tuning the transmission powers of hosts to control the structure of the network. The target topology includes 1-edge-, 1-vertex-, 2-edge-, and 2-vertex-connected graphs. The goal is to maximize the lifetime of the network, i.e., the amount of time when all hosts remain alive. Two variations of the problem, where hosts' powers can be fixed or variable during the lifetime of the network, are discussed. We show that optimal lifetimes can be obtained by using a simple minimum spanning tree construction under the fixed power assumption.