In wireless network, fault tolerant topology control is an important and a challenging task. The wireless nodes and links could experience frequent failures since Wireless networks are usually deployed under extreme environments. Therefore, fault tolerance must be considered for many applications. In wireless network Topology control has been proved effective in saving node power. The main idea of topology control is that instead of using its maximal transmission power, each node sets its power to a certain level such that the global topology satisfies a certain constraint. To increase fault tolerance, nodes in the network will consume more power. Here we need to give the optimum distance between the nodes of the wireless network in order to reduce the consumption of the power of each node. This paper deals with the approach for the finding the minimum distance between the nodes of the wireless network by the use of mat lab coding through the graph theory considering the minimum weight based algorithm.