Due to the nodes' limited resource in the wireless ad hoc networks, the scalability is crucial for network operations. One effective approach is to maintain only a linear number of links. However, this sparseness should not compromise too much on the power consumptions on communications such as unicasting, or multicasting. For any topology $G$, its unicasting power stretch factor is defined as the maximum ratio of the minimum power needed to support any link in $G$ to the least necessary. We consider a wireless ad hoc network consisting of a set of nodes $V$ distributed in a two-dimensional plane modeled by the unit disk graph. We consider several well-known proximity graphs including relative neighborhood graph, Gabriel graph and Yao graph and their combinations for constructing the wireless network topology. These graphs are sparse and can be constructed locally in an efficient way. Notice that all of these graphs do not have constant degrees. We present some new algorithms to construct a sparse and power efficient topology. We conduct experiments to show that the unicasting power stretch factor is also very small practically. We also show how to combine the Yao graph structure, the Gabriel graph structure to increase the sparseness of the topology without affecting the power efficiency of the constructed network.