TY - JOUR
ID - 13846
TI - On independent domination numbers of grid and toroidal grid directed graphs
JO - Communications in Combinatorics and Optimization
JA - CCO
LA - en
SN - 2538-2128
AU - Shaheen, Ramy
AD - ٍSyrian
Y1 - 2019
PY - 2019
VL - 4
IS - 1
SP - 71
EP - 77
KW - directed path
KW - directed cycle
KW - Cartesian product
KW - independent domination number
DO - 10.22049/cco.2019.26282.1090
N2 - 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.
UR - http://comb-opt.azaruniv.ac.ir/article_13846.html
L1 - http://comb-opt.azaruniv.ac.ir/article_13846_0948ec1c34ebfc23d9e6b9f6dc3f735d.pdf
ER -