June 10, 2023
Doost Ali Mojdeh

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


Title On three outer-independent domination related parameters in graphs
Type Article
Total outer-independent domination, 2-outer-independent domination, Double outer-independent domination, Nordhaus–Gaddum inequality
DOI https://doi.org/10.1016/j.dam.2021.01.027
Researchers Doost Ali Mojdeh (First researcher) , Iztok Peterin (Second researcher) , Babak Samadi (Third researcher) , Ismael Gonzalez Yero (Fourth researcher)


Given a graph $G$, a set of vertices $S\subseteq V(G)$ is a (resp. total or double) $2$-outer independent dominating set, if $S$ is a (resp. total or double) $2$-dominating set whose complement is an independent set. The (resp. total or double) $2$-outer independent domination number of $G$ is the smallest possible cardinality of a (resp. total or double) $2$-outer independent dominating set of $G$. In this paper, the $2$-outer independent, the total outer independent and the double outer independent domination numbers of graphs are investigated. We make some comparisons among these three domination parameters and bound their values from above and below. Moreover, we prove some Nordhaus-Gaddum type inequalities for them and present some complexity issues concerning finding their values.