In a dense environment, wireless sensor network (WSN) requires more energy to work in an effective and efficient manner. Hence, energy conservation is the main objective. In the paper, we have proposed a methodology to construct a backbone using modular antennas in combination with spanning tree protocol (STP), graph sampling, and Connecting Dominating Set (CDS) strategy. The backbone construction is based upon the modular antenna based WSNs, where the dominating sets can avoid the intermediate connection in order to reduce the hop count and energy consumption. The dominating sets have been connected using the modular transmission range of the wireless sensor networks to construct the backbone. The dominating set selection procedure to construct the WSN backbone is based upon the degree of connections of the nodes, which enables the locally centralized behavior of the connected dominating sets. The proposed methodology has been proved effective resulting in the construction of an energy efficient backbone.