Domatic Number of Graph Products
نویسندگان
چکیده
A partition of V (G), all of whose classes are 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 number of G. The concept of a domatic number was introduced in [1]. More interesting results on domatically full graphs, domatically critical, domatically cocritical graphs and other domatic numbers can be found in [3], [4], [5], [6], [7]. We explore the bounds the domatic number of the cartesian product, the strong product and the corona of two graphs. The join of two graphs and its generalization also is studied. Motivation of this problem comes from [2], where the domatic number of the cartesian product of two paths was established.
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