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Nodes in energy-efficient ad-hoc wireless networks can benefit more of new ad-hoc services, as well as, can support better new emerging ad-hoc applications. In this paper, we introduce an approach to achieve the energy efficiency based on both optimal transmission range and topology management of ad-hoc wireless networks. We derive the relationship between the optimal transmission range (optimal grid length) and different intensities of static network traffic in the equal-grid rectangular GAF (the geographical adaptive fidelity topology management protocol) network and implement this result into dynamic network traffic scenario with adjustable-grid rectangular GAF network to achieve the energy efficiency. Then we compare the energy consumption result of adjustable-grid model to the result of traditional GAF model (equal-grid), which is derived in the same dynamic traffic scenario.Our results show that the adjustable-grid model saves 78.1% energy in comparison to the minimum energy consumption of equal-grid model.