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/