Nordhaus-Gaddum type inequalities for multiple domination and packing parameters in graphs
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. As the special case $(k-1, k, j)=(1, 2, 0) $ we give an
upper bound on $ dd (G)+ dd (\overline {G}) $ stronger than that 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.
of a graph $ G $ and investigate these bounds for the $ k $-limited packing and $ k $-total
limited packing numbers in graphs. As the special case $(k-1, k, j)=(1, 2, 0) $ we give an
upper bound on $ dd (G)+ dd (\overline {G}) $ stronger than that 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.
We study the Nordhaus-Gaddum type results for and -domination numbers of a graph and investigate these bounds for the -limited packing and -total limited packing numbers in graphs. As the special case we give an upper bound on stronger than that 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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