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Doost Ali Mojdeh

Doost Ali Mojdeh

Academic rank: Professor
ORCID:
Education: PhD.
ScopusId:
Faculty: Faculty of Mathematical Sciences
Address: Department of Mathematics, University of Mazandaran, Babolsar, Iran
Phone: 011-35302448

Research

Title
NORDHAUS-GADDUM INEQUALITIES FOR DOMINATION AND PACKING PARAMETERS IN GRAPHS
Type
Presentation
Keywords
Nordhaus-Gaddum inequality, open packing number, packing number, total domination number
Year
2017
Researchers Doost Ali Mojdeh ، Babak Samadi

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.