Domination in Bipartite Graphs and in Their Complements

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The domatic numbers of a graph G and of its complement were studied by J. E. Dunbar, T. W. Haynes and M. A. Henning. They suggested four open problems. We will solve the following ones:Characterize bipartite graphs G having d(G) = d()Further, we will present a partial solution to the problem:Is it true that if G is a graph satisfying d(G) = d() then γ(G) = γ()Finally, we prove an existence theorem concerning the total domatic number of a graph and of its complement

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