Let  be a simple connected graph. A subset M of E(G) is a perfect edge dominating set of G if every edge not in M is adjacent to exactly one edge in M. The perfect edge domination number of G denoted by  is the minimum cardinality of a perfect edge dominating set of G. Moreover, any perfect edge dominating set of G with cardinality  is referred to as a -set of G. In this paper, the researcher investigates the concept of the perfect edge domination in a graph and obtains some results involving the concepts of edge domination and perfect edge domination.

domination, edge domination, perfect edge domination.