# On independent domination numbers of grid and toroidal grid directed graphs

Document Type : Original paper

Author

ٍSyrian

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

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