  A subset $D\subseteq V(G)$ is called a $k$-distance dominating set of $G$ if
every vertex in $V(G)\setminus D$ is within distance $k$ from some vertex of
$D$. The minimum cardinality among all $k$-distance dominating sets of $G$ is
called the $k$-distance domination number of $G$. In this note we give upper
bound on the $k$-distance domination number of a connected bipartite graph and
improve some results have been given like Theorem 2.1 and 2,7 in [Tian and Xu,
A note on distance domination of graphs, Australian Journal of Combinatorics,
43 (2009), 181-190].
