Geodesic
On the b -Domatic Number of Graphs
Discussiones Mathematicae. Graph Theory, Tome 39 (2019) no. 2, pp. 313-324

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A set of vertices S in a graph G = (V, E) is a dominating set if every vertex not in S is adjacent to at least one vertex in S. A domatic partition of graph G is a partition of its vertex-set V into dominating sets. A domatic partition P of G is called b-domatic if no larger domatic partition of G can be obtained from P by transferring some vertices of some classes of P to form a new class. The minimum cardinality of a b-domatic partition of G is called the b-domatic number and is denoted by bd(G). In this paper, we explain some properties of b-domatic partitions, and we determine the b-domatic number of some families of graphs.
Keywords: domatic partition, domatic number, b-domatic partition, b-domatic number 
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Benatallah, Mohammed; Ikhlef-Eschouf, Noureddine; Mihoubi, Miloud. On the b -Domatic Number of Graphs. Discussiones Mathematicae. Graph Theory, Tome 39 (2019) no. 2, pp. 313-324. http://geodesic.mathdoc.fr/item/DMGT_2019_39_2_a1/