@article {
author = {Shaheen, Ramy},
title = {On independent domination numbers of grid and toroidal grid directed graphs},
journal = {Communications in Combinatorics and Optimization},
volume = {4},
number = {1},
pages = {71-77},
year = {2019},
publisher = {Azarbaijan Shahid Madani University},
issn = {2538-2128},
eissn = {2538-2136},
doi = {10.22049/cco.2019.26282.1090},
abstract = {A subset $S$ of vertex set $V(D)$ is an indpendent dominating set of $D$ if $S$ is both an independent and a dominating set of $D$. The indpendent domination number, $i(D)$ is the cardinality of the smallest independent dominating set of $D$. In this paper we calculate the independent domination number of the cartesian product of two directed paths $P_m$ and $P_n$ for arbitraries $m$ and $n$. Also, we calculate the independent domination number of the Cartesian product of two directed cycles $C_m$ and $C_n$ for $m, n \equiv 0\pmod 3$, and $n \equiv 0\pmod m$. There are many values of $m$ and $n$ such that $C_m \Box C_n$ does not have an independent dominating set.},
keywords = {directed path,directed cycle,Cartesian product,independent domination number},
url = {http://comb-opt.azaruniv.ac.ir/article_13846.html},
eprint = {http://comb-opt.azaruniv.ac.ir/article_13846_0948ec1c34ebfc23d9e6b9f6dc3f735d.pdf}
}