@article {
author = {Aram, H. and Sheikholeslami, S. M. and Volkmann, L.},
title = {On the total domatic number of regular graphs},
journal = {Transactions on Combinatorics},
volume = {1},
number = {1},
pages = {45-51},
year = {2012},
publisher = {University of Isfahan},
issn = {2251-8657},
eissn = {2251-8665},
doi = {10.22108/toc.2012.760},
abstract = {A set $S$ of vertices of a graph $G=(V,E)$ without isolated vertex is a total dominating set if every vertex of $V(G)$ is adjacent to some vertex in $S$. The total domatic number of a graph $G$ is the maximum number of total dominating sets into which the vertex set of $G$ can be partitioned. We show that the total domatic number of a random $r$-regular graph is almost surely at most $r-1$, and that for 3-regular random graphs, the total domatic number is almost surely equal to 2. We also give a lower bound on the total domatic number of a graph in terms of order, minimum degree and maximum degree. As a corollary, we obtain the result that the total domatic number of an $r$-regular graph is at least $r/(3\ln(r))$.},
keywords = {total dominating set,total domination number,total domatic number,Regular graph},
url = {https://toc.ui.ac.ir/article_760.html},
eprint = {https://toc.ui.ac.ir/article_760_362cc9c41ad1def424bd149103450c49.pdf}
}