EDGE DOMATIC NUMBERS OF COMPLETE N-PARTITE GRAPHS

Abstract

An edge dominating set of a graph is a set of edges D such that every edge not in D is adjacent to an edge in 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 of G. In this paper we study the edge domatic numbers of complete n-partite graphs. In particular, we give exact values for the edge domatic numbers of complete 3-partite graphs and balanced complete n-partite graphs with odd n.