(untitled) (Damascus University Journal for the basic sciences, 2025)
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. Wireless sensors network are tiny battery-powered devices. The energy is one of bounded materials in wireless sensor networks which plays effective role in prformance of these networks. In Mathematics, a network is an example of a graph the integrating process of graph theory with wireless networks is considered a significant issue in the scientific research filed. But not all the network emerge organizely wheresome ones emerge spontaneously or unorganizely and they devlope gradually throug time. Which led to the definition of the random graph. So in our work we aim to get knowledge about random graph and then broaching to random geometric graph. Also we suggest new model for building randomly deployed wireless sensor networks. The suggested model is effective with respect to time complexiction for contructing network (O(n2)) . on the other hand it works on decreasing of energy consumptiun by using geometric random graph. For ensuring of validity of results we ran a simulation of the model in work environment Matlab.