Nordhaus-Gaddum type inequalities for multiple domination and packing parameters in graphs, By Doost Ali Mojdeh

Research

Title	Nordhaus-Gaddum type inequalities for multiple domination and packing parameters in graphs
Type	Article
Keywords	k-domination number, Nordhaus{Gaddum inequality, open packing number, packing number, total domination number.
Journal	Contributions to Discrete Mathematics
DOI	DOI: https://doi.org/10.11575/cdm.v15i1.62630
Researchers	Doost Ali Mojdeh (First researcher) , Babak Samadi (Second researcher) , Lutz Volkmann (Third researcher)

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(¯¯¯¯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.