%0 Journal Article
%T On Signed Domination of Grid Graph
%A Mohammad Hassan
%A Muhsin Al Hassan
%A Mazen Mostafa
%J Open Journal of Discrete Mathematics
%P 96-112
%@ 2161-7643
%D 2020
%I Scientific Research Publishing
%R 10.4236/ojdm.2020.104010
%X Let <em>G</em>(<em>V</em>, <em>E</em>) be a finite connected simple graph with vertex set <em>V</em>(<em>G</em>). A function   is a signed dominating function <em>f </em>:&nbsp;<em style=\"white-space:normal;\">V</em><span style=\"white-space:normal;\">(</span><em style=\"white-space:normal;\">G</em><span style=\"white-space:normal;\">)</span><span style=\"white-space:nowrap;\">¡ú{<span style=\"white-space:nowrap;\"><span style=\"white-space:nowrap;\">&amp;minus;</span></span>1,1}</span> if for every vertex <em>v</em> <span style=\"white-space:nowrap;\">¡Ê</span> <em>V</em>(<em>G</em>), the sum of closed neighborhood weights of <em>v</em> is greater or equal to 1. The signed domination number <em>¦Ã</em><sub>s</sub>(<em>G</em>) of <em>G</em> is the minimum weight of a signed dominating function on <em>G</em>. In this paper, we calculate the signed domination numbers of the Cartesian product of two paths <em>P</em><sub><em>m</em></sub> and <em>P</em><sub><em>n</em></sub> for <em>m</em> = 6, 7 and arbitrary <em>n</em>.
%K Grid Graph
%K Cartesian Product
%K Signed Dominating Function
%K Signed Domination Number
%U http://www.scirp.org/journal/PaperInformation.aspx?PaperID=103681