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.
@article{bwmeta1.element.doi-10_7151_dmgt_1996, author = {Saieed Akbari and Mohammad Motiei and Sahand Mozaffari and Sina Yazdanbod}, title = {Cubic Graphs with Total Domatic Number at Least Two}, journal = {Discussiones Mathematicae Graph Theory}, volume = {38}, year = {2018}, pages = {75-82}, language = {en}, url = {http://dml.mathdoc.fr/item/bwmeta1.element.doi-10_7151_dmgt_1996} }
Saieed Akbari; Mohammad Motiei; Sahand Mozaffari; Sina Yazdanbod. Cubic Graphs with Total Domatic Number at Least Two. Discussiones Mathematicae Graph Theory, Tome 38 (2018) pp. 75-82. http://gdmltest.u-ga.fr/item/bwmeta1.element.doi-10_7151_dmgt_1996/