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A De Brujin graph (DBG) model is proposed to apply to enhance communication robustness and to improve energy reliability and efficiency in smart grids. This fault tolerant model can avoid wire communication faults among smart meters by an alternative wireless resilient Zigbee scheme. As a result, this communication model can also search optimized wireless resilience paths to enhance communication fault tolerance. The experimental results show 100% communication fault tolerance in all smart grid regions based on single fault assumption. While for multiple link fault tolerance, our proposed FTGDB scheme could averagely tolerate more than 30% faulty links simultaneously.