Abstract
A function $f:V(G)rightarrow {-1,0,1}$ is a minus dominating function if for every vertex $vin V(G)$, $sum_{uin N[v]}f(u)ge 1$. A minus dominating function $f$ of $G$ is called a global minus dominating function if $f$ is also a minus dominating function of the complement $overline{G}$ of $G$. The global minus domination number $gamma_{g}^-(G)$ of $G$ is defined as $gamma_{g}^-(G)=min{sum_{vin V(G)} f(v)mid f ;{rm is; a; global; minus; dominating; function} {rm of }; G}$. In this paper we initiate the study of the global minus domination number in graphs and we establish lower and upper bounds for the global minus domination number.
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