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On independent domination numbers of grid and toroidal grid directed graphs | ||
| Communications in Combinatorics and Optimization | ||
| مقاله 7، دوره 4، شماره 1، شهریور 2019، صفحه 71-77 اصل مقاله (375.61 K) | ||
| نوع مقاله: Original paper | ||
| شناسه دیجیتال (DOI): 10.22049/cco.2019.26282.1090 | ||
| نویسنده | ||
| Ramy Shaheen* | ||
| ٍSyrian | ||
| چکیده | ||
| 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. | ||
| کلیدواژهها | ||
| directed path؛ directed cycle؛ Cartesian product؛ independent domination number | ||
| مراجع | ||
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