|
Abstract
|
We study the Nordhaus-Gaddum type results for $(k,k,j)$ and investigate them for the $k$-limited packing and $k$-total limited packing numbers in graphs. As the special cases $(k,k,j)=(1,1,0)$ and $(k,k,j)=(1,2,0)$ we give upper bounds on $\gamma_{t}(G)+\gamma_{t}(\overline{G})$ and $\gamma_{\times2}(G)+\gamma_{\times2}(\overline{G})$, respectively, stronger than those conjectured by Harary and Haynes (1996). Moreover, we establish upper bounds on the sum and product of packing and open packing numbers and characterize all graphs attaining these bounds.
|