  In this paper, we find upper bounds on the open packing and $k$-limited
packing numbers with emphasis on the cases $k=1$ and $k=2$. We solve the
problem of characterizing all connected graphs on $n$ vertices with
$\rho_{o}(G)=n/\delta(G)$ which was presented in 2015 by Hamid and
Saravanakumar. Also, by establishing a relation between the $k$-limited packing
number and double domination number we improve two upper bounds given by
Chellali and Haynes in 2005.
