  The first multiplicative Zagreb index $\Pi_1$ of a graph $G$ is the product
of the square of every vertex degree, while the second multiplicative Zagreb
index $\Pi_2$ is the product of the products of degrees of pairs of adjacent
vertices. In this paper, we give sharp lower bound for $\Pi_1$ and upper bound
for $\Pi_2$ of trees with given distance $k$-domination number, and
characterize those trees attaining the bounds.
