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The advent of wireless communication and networking in the last two decades has led to the need of modification in the regular graphs used as spanners. The spanner is a sub graph of the original graph which connects the essential nodes for transmission of the message. For this purpose the Omni directional antennas are usually used and the “spanner-graph” performance metric is a constant multiplied by the same of the original graph. This constant is known as the “stretch factor”. One of the most common attribute for wireless communication is the energy required for faithful transmission of a message between two nodes. But the Omni directional antennas lead to interference and wastage of bandwidth and energy. The nodes of wireless communication are however neither always static nor equipped with any infrastructure. Rather the same might as well be ad-hoc and mobile. Another well used notion is that of the unit disk graph (UDG), where a node can communicate INTERNATIONAL JOURNAL ON SMART SENSING AND INTELLIGENT SYSTEMS VOL. 7, NO. 2, June 2014

A Review Of Energy Optimal Topology Control For Large Wireless Network Using Yao-Graph And Its Variants