We construct reliable connected dominating set in wireless ad hoc networks. Unlike previous techniques, the choice of dominators in these schemes, are based not on node characteristics but on the link characteristics. We define the link reliability as the association of link stability and packet error rate. We propose different distributed heuristic algorithms, enhanced marking, high-reliability and recommendation algorithm. To compare with distributed algorithms, we also propose a centralized algorithm, minimum energy tree-growing algorithm. Through performance evaluation, we show that high-reliability scheme is the best results in the distributed algorithm. Our simulations show the proposed algorithms increase few CDS sizes of existing algorithm and decrease the energy cost that means packet retransmissions.