  Let $\gamma(G)$ and $\gamma_t(G)$ denote the domination number and the total
domination number, respectively, of a graph $G$ with no isolated vertices. It
is well-known that $\gamma_t(G) \leq 2\gamma(G)$. We provide a characterization
of a large family of graphs (including chordal graphs) satisfying $\gamma_t(G)=
2\gamma(G)$, strictly generalizing the results of Henning (2001) and Hou et al.
(2010), and partially answering an open question of Henning (2009).
