Wireless sensor networks are considered one of the most important applications in mobile computing and networking. These networks play an important role in our daily life. However, wireless sensor networks have a lot of vital purposes in modern technology, such as scientific research, rescue operations, and scientific discoveries. The energy power consumption of wireless sensor networks is considered a significant issue because of their relationship with live mode. Therefore, sensor devices are heavily based on modern schemes to save its energy power consumption. In this case, any random response of sensor nodes will have a direct and negative impact on devices' life. In this paper, a novel scheme is proposed to manage consumption energy rate of sensor devices. It is heavily depended on graph theory in control/ management on amount of power consumption per time. This technique will enable mobility sensor nodes stay at waiting in sleep mode to obtain new information/ control data at certain time for response / moving from one location to another under radio coverage area. Thus, the mathematical model is employed in positioned wireless sensor nodes. In addition, graph theory has the ability to identify sensor nodes movement without energy power losses. Our experimental results of the proposed system show that graph theory sensor devices possess outstanding results with a significant reducing in the amount of energy power consumption for sensors.