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Since there is no fixed infrastructure or centralized management in wireless sensors networks (WSNs), a connected dominating set (CDS) has been proposed as the virtual backbone. The CDS play a major role in routing, broadcasting, coverage and activity scheduling. To reduce the traffic during communication and prolong network lifetime, it is desirable to construct a minimum CDS (MCDS). Self-stabilization is a theoretical framework of non-masking fault tolerant distributed algorithms. A self stabilizing system tolerates any kind and any finite number of transient faults, such as power termination, message loss, memory corruption, and topology change. There are few publications dealing with self-stabilizing MCDS (SSMCDS) where all of them, the network has been modeled in Unit Disk Graph (UDG), in which each node has the same transmission range. In real world this kind of networks are not necessarily contain nodes with similar transmission range. As a new approach, network has been modeled by disk graph with bidirectional links (DGB), in which nodes have different transmission range. In this paper has presented a new distributed approximation algorithm for SS-MCDS problem in DGB (called SS-MCDS-DGB) with constant approximation ratio and O(n2) time complexity using unfair central daemon.