Nordhaus-Gaddum type inequalities for multiple domination and packing parameters in graphs

Contributions to Discrete Mathematics, vol. 15, pp. 154–162

Abstract

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.

Authors 3

1. Doost Ali Mojdeh corresponding

   University of Mazandaran

   Affiliation as printed

   Department of Mathematics University of Mazandaran, Babolsar, Iran

2. Babak Samadi

   University of Mazandaran

   Affiliation as printed

   University of Mazandaran

   University of Mazandaran,

3. Lutz Volkmann Aachen Lehrstuhl II für Mathematik

   RWTH Aachen University

   Affiliation as printed

   Lehrstuhl II für Mathematik RWTH Aachen University, 52056 Aachen, Germany