February 9, 2023

# Doost Ali Mojdeh

Degree: Professor
Address: Department of Mathematics, University of Mazandaran, Babolsar, Iran
Education: Ph.D in Mathematics (Graph Theory and Combinatorics)
Phone: 011-35302448
Faculty: Faculty of Mathematical Sciences

## 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 Researchers a { color: #4f98b0; } a:hover { color: #ffab00; } a:link:visited { text-decoration: none; } Babak Samadi (First researcher) , Doost Ali Mojdeh (Second researcher)

## 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.