Geodesic
Total domination of Cartesian products of graphs
Discussiones Mathematicae. Graph Theory, Tome 27 (2007) no. 1, pp. 175-178

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Let γₜ(G) and γ_pr(G) denote the total domination and the paired domination numbers of graph G, respectively, and let G □ H denote the Cartesian product of graphs G and H. In this paper, we show that γₜ(G)γₜ(H) ≤ 5γₜ(G □ H), which improves the known result γₜ(G)γₜ(H) ≤ 6γₜ(G □ H) given by Henning and Rall.
Keywords: total domination number, Cartesian product, Vizing's conjecture 
Hou, Xinmin. Total domination of Cartesian products of graphs. Discussiones Mathematicae. Graph Theory, Tome 27 (2007) no. 1, pp. 175-178. http://geodesic.mathdoc.fr/item/DMGT_2007_27_1_a14/
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