Cubic Graphs with Total Domatic Number at Least Two
Abstract
Let $G$ be a graph. 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 would like to characterize the cubic graphs with total domatic number at least two.
 Publication:

arXiv eprints
 Pub Date:
 December 2015
 arXiv:
 arXiv:1512.04748
 Bibcode:
 2015arXiv151204748A
 Keywords:

 Mathematics  Combinatorics;
 Computer Science  Discrete Mathematics
 EPrint:
 6 pages, 5 figures