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Domatic number of graph products

Kijewska M.

Journal of Mathematics and Applications

2008

Vol. 30

71-81

A partition of V(G), all of whose classes arę dominating sets in G, is called a domatic partition of G. The maximum number of classes of a domatic partition of G is called the domatic nuraber of G. In this paper we explore the bounds for the domatic numbers of the cartesian product, the strong product and the join of two graphs. The bounds are the best possible in the sense that there exist examples for which equalities are attained.