Abstract-One of the fundamental issues in WSN is the design of energy efficient approaches that achieve full area coverage and maintain the connectivity of the whole network. Coverage reflects how well a sensor field is monitored. In order to monitor the area of interest in the most efficient way, finding the connected covered sub-regions allows the use of Sleep scheduling techniques that put cooperatively the nodes monitoring these areas into sleep-mode without increasing the response time of the network. In our work, we use the idea of graph theory and we propose a new method called Net Arcs (NA) that transform the graph model from theory state to the real time. We use some techniques to find the all overlapped covered sub-regions (2-Edges) and (3-Edges) and we ensure the connectivity of the network by finding the maximum covered regions. Finding these sub-regions increases WSN lifetime and provides improved coverage performance.