Geodesic
Cubic Graphs with Total Domatic Number at Least Two
Discussiones Mathematicae. Graph Theory, Tome 38 (2018) no. 1, pp. 75-82.

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Let G be a graph with no isolated vertex. A total dominating set of G is a set S of vertices of G such that every vertex is adjacent to at least one vertex in S. The total domatic number of a graph is the maximum number of total dominating sets which partition the vertex set of G. In this paper we provide a criterion under which a cubic graph has total domatic number at least two.
Keywords: total domination, total domatic number, coupon coloring 
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Akbari, Saieed; Motiei, Mohammad; Mozaffari, Sahand; Yazdanbod, Sina. Cubic Graphs with Total Domatic Number at Least Two. Discussiones Mathematicae. Graph Theory, Tome 38 (2018) no. 1, pp. 75-82. http://geodesic.mathdoc.fr/item/DMGT_2018_38_1_a5/

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