On Total Domination in the Cartesian Product of Graphs

@article{Bresar2018OnTD,
title={On Total Domination in the Cartesian Product of Graphs},
author={B. Bresar and Tatiana Romina Hartinger and T. Kos and Martin Milani{\vc}},
journal={Discussiones Mathematicae Graph Theory},
year={2018},
volume={38},
pages={963 - 976}
}

Abstract Ho proved in [A note on the total domination number, Util. Math. 77 (2008) 97–100] that the total domination number of the Cartesian product of any two graphs without isolated vertices is at least one half of the product of their total domination numbers. We extend a result of Lu and Hou from [Total domination in the Cartesian product of a graph and K2 or Cn, Util. Math. 83 (2010) 313–322] by characterizing the pairs of graphs G and H for which γt(G□H)=12γt(G)γt(H) $\gamma _t \left( {G… Expand