In wireless sensor networks (WSNs), the energy source is usually a battery cell, which is impossible to recharge while WSNs are working. Therefore, one of the main issues in wireless sensor networks is how to prolong the network lifetime of WSNs with certain energy sources as well as how to maintain coverage and connectivity. In this paper, we consider wireless sensor networks satisfying the case that each node either monitors one target or is just for connection. Assume that the wireless sensor network has l targets, and that each is monitored by k sensor nodes. If k = 2 and the graph G corresponding to the wireless sensor network is ( l + max { 1 , l − 4 } ) -connected, or k ≥ 3 and G is ( l ( k − 1 ) + 1 ) -connected, then we can find k (the maximum number) disjoint sets, each of which completely covers all the targets and remains connected to one of the central processing nodes. The disjoint sets are activated successively, and only the sensor nodes from the active set are responsible for monitoring the targets and connectivity; all other nodes are in a sleep mode. In addition, we also give the related algorithms to find the k disjoint sets.