Recently, many large-scale natural disasters, such as earthquake and tsunami occur all over the world. One of the major problems after a disaster is the damage caused to the communication and power infrastructure, such as damaged base station and power grid. As a result, disaster victims are unable to communicate with outside area for an extended period of time. Therefore, it is essential to deploy a communication network, which can operate even without power supply or infrastructure. In this paper, we focus on Wireless Mesh Networks (WMNs), which consists of Solar Powered Base Station (SPBS) equipped with air interfaces. These WMNs can be promptly setup. However, because the power generated from solar panel is easily affected by weather condition, it is insufficient and unstable. Additionally, because the power consumption is affected by the distance between the SPBSs and the number of wireless links in each SPBS, it is difficult to maintain network connectivity in the WMNs that are consisted of SPBSs. Therefore, to address the network connectivity problem in the assumed network, we aim to reduce the power consumption of the wireless links by controlling the on-off cycle of air interfaces. We first analyze the network connectivity issue in disaster area and formulate this problem, and propose the on-off scheme of controlling the wireless links of air interfaces based on graph theory. Simulation results of our proposal show that our proposed scheme can ensure the network connectivity.