%0 Journal Article
%T On the 2-Domination Number of Complete Grid Graphs
%A Ramy Shaheen
%A Suhail Mahfud
%A Khames Almanea
%J Open Journal of Discrete Mathematics
%P 32-50
%@ 2161-7643
%D 2017
%I Scientific Research Publishing
%R 10.4236/ojdm.2017.71004
%X A set <em>D</em> of vertices of a graph <em>G</em> = (<em>V</em>, <em>E</em>) is called <em>k</em>-dominating if every vertex<span style=\"white-space:nowrap;\"> <em>v </em>¡Ê<em>V</em><em>-D</em></span> is adjacent to some <em>k</em> vertices of <em>D</em>. The <em>k</em>-domination number of a graph <em>G</em>, <span style=\"white-space:nowrap;\">¦Ã<sub>k</sub></span> (<em>G</em>), is the order of a smallest <em>k</em>-dominating set of <em>G</em>. In this paper we calculate the <em>k</em>-domination number (for <em>k</em> = 2) of the product of two paths <em>P</em><sub>m</sub> ¡Á <em>P</em><sub>n</sub> for <em>m</em> = 1, 2, 3, 4, 5 and arbitrary n. These results were shown an error in the paper [1].
%K &lt
%K i&gt
%K k&lt
%K /i&gt
%K -Dominating Set
%K &lt
%K i&gt
%K k&lt
%K /i&gt
%K -Domination Number
%K 2-Dominating Set
%K 2-Domination  Number
%K Cartesian Product Graphs
%K Paths
%U http://www.scirp.org/journal/PaperInformation.aspx?PaperID=73747