The main purpose of computer networks offer many advantages including communication connected pipe lines and collaboration resource sharing the pair of intervals from ai to bi, centralized data management like dominating sets, perfect odd vertices dominating sets, remote access , automation reduced costs. The use of dominating sets improved customer service and real time monitoring and control. Another common reason for connectivity issues is data server failure. Router issues can also be the source of the problem. Any equipment failure can lead to a complete network failure.the study of...