On a Class of Graphs with Large Total Domination Number

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) <= 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 and Xu (2010), and partially answering an open question of Henning (2009).