For connected isolate-free graphs, the paper proves several upper and lower bounds on the total domination number in terms of the domination and connected domination numbers, and conjectures a sharper lower bound.
On the domination of the products of graphs ii: trees.Journal of graph theory, 10(1):97–106, 1986
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A Note on Inequalities for Three Domination Parameters
For connected isolate-free graphs, the paper proves several upper and lower bounds on the total domination number in terms of the domination and connected domination numbers, and conjectures a sharper lower bound.