THE DOMATIC NUMBER PROBLEM

Abstract

A dominating set of a graph G=(V,E) is a subset D of V such that every vertex not in D is adjacent to some vertex in D. The domatic number d(G) of G is the maximum positive integer k such that V can be partitioned into k pairwise disjoint dominating sets. The purpose of this paper is to study the domatic numbers of graphs that are obtained from small graphs by performing graph operations, such as union, join and Cartesian product.