[Note: Now reopened!]
The question concerns the limit as $n\to\infty$ of $\gamma_t(Q_n)/n$. It is known to be between $\frac{4}{7}$ and $\frac{2}{3}$.
As connected and total domination the queen's graph have been studied together by Hedetniemi and Ameridabi in 2005, I mentioned my new formation of queens which provides connected and total dominating sets for $n$ is divisible by $6$. This formation provides the best known upper bound for $n$ divisible by $6$ and $n$ sufficiently large. Thus, the newer formation was used as an example along with my mentioning of Welsch's formation.
This is publishable material I feel that I've chosen to share. However, as I'm no longer an academic, I prefer mathoverflow for recreational questions like these.
Please take a look and consider it!
