Edge domination in complete partite graphs

Abstract An 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 .