Nordhaus-Gaddum type inequalities for multiple domination and packing parameters in graphs
DOI:
https://doi.org/10.11575/cdm.v15i1.62630Abstract
We study the Nordhaus-Gaddum type results for $(k-1,k,j)$ and $k$-domination numbers of a graph $G$ and investigate these bounds for the $k$-limited packing and $k$-total limited packing numbers in graphs with emphasis on the case $k=1$. In the special case $(k-1,k,j)=(1,2,0)$, we give an upper bound on $dd(G)+dd(\overline{G})$ stronger than the bound presented 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.
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