On the packing numbers in graphs
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 $ρ_{o}(G)=n/δ(G)$ 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.
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