$k$-Tuple Total Domination Number of Cartesian Product Graphs

Adel P. Kazemi, Behnaz Pahlavsay

Published 2015-09-28Version 1

The most famous open problem involving domination in graphs is Vizing's conjecture which states the domination number of the Cartesian product of any two graphs is at least as large as the product of their domination numbers. In this paper, we investigate a similar problem for the k-tuple total domination number. Then we calculate the k-tuple total domination number of the Cartesian product of two complete graphs.