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 ρo(G) = n/δ(G) which was raised in 2015 by Hamid and Saravanakumar. Also, by establishing a relationship between the k-limited packing number and double domination number we improve two upper bounds given by Chellali and Haynes in 2005.
