Connected Graphs with Maximum Total Domination Number

The total domination number \(\gamma_t(G)\) of graph \(G = (V, E)\) is the cardinality of a smallest subset \(S\) of \(V\) such that every vertex of \(V\) has a neighbor in \(S\). It is known that, if \(G\) is a connected graph with \(n\) vertices, \(\gamma_t(G) \leq \left\lfloor{2n}/{3}\right\rfloor\). Graphs achieving this bound are characterized.