Edge domination in complete partite graphs

AbstractAn edge dominating set in a graph G is a set of edges D such that every edge not in D is adjacent to an edge of D. An edge domatic partition of a graph G=(V,E) is a collection of pairwise-disjoint edge dominating sets of G whose union is E. The maximum size of an edge domatic partition of G is called the edge domatic number. In this paper, we study the edge domatic number of the complete partite graphs and give the answers for balanced complete partite graphs and complete split graphs