Graph theory has grown in importance in applied mathematics as a result of its wide range of applications and utility. Geometry, algebra, number theory, topology, optimization, and computer science all employ graph theory to solve combinatorial issues. Both graph theory and applications rely on the concept of connectedness. Power domination is a generalization of the optimization method in which measuring devices in the specified field are put at precise spots in electronic and electrical power networks. In mathematics, graphs are used to define networks. The classic vertex cover problem and domination problem in graph theory are strongly related to monitoring an electric power system with as few phase measuring units (PMUs) as possible. If every vertex and every edge in the system are seen using the observation criteria of power system monitoring, a set S is a power dominant set (PDS) of a graph G. Thus, the concept of power domination in Strong and Complete graph is established using theorems and examples.