  A vertex $u$ in a graph $G$ totally dominates a vertex $v$ if $u$ is adjacent
to $v$ in $G$. A total dominating set of $G$ is a set $S$ of vertices of $G$
such that every vertex of $G$ is totally dominated by a vertex in $S$. The
indicated total domination game is played on a graph $G$ by two players,
Dominator and Staller, who take turns making a move. In each of his moves,
Dominator indicates a vertex $v$ of the graph that has not been totally
dominated in the previous moves, and Staller chooses (or selects) any vertex
adjacent to $v$ that has not yet been played, and adds it to a set $D$ that is
being built during the game. The game ends when every vertex is totally
dominated, that is, when $D$ is a total dominating set of $G$. The goal of
Dominator is to minimize the size of $D$, while Staller wants just the
opposite. Providing that both players are playing optimally with respect to
their goals, the size of the resulting set $D$ is the indicated total
domination number of $G$, denoted by $\gamma_t^{\rm i}(G)$. In this paper we
present several results on indicated total domination game. Among other results
we prove that the indicated total domination number of a graph is bounded below
by the well studied upper total domination number.
