Global minus domination in graphs

A function $f:v(g)rightarrow {-1,0,1}$ is a {em minusdominating function} if for every vertex $vin v(g)$, $sum_{uinn[v]}f(u)ge 1$. a minus dominating function $f$ of $g$ is calleda {em global minus dominating function} if $f$ is also a minusdominating function of the complement $overline{g}$ of $g$. the{em global minus domination number} $gamma_{g}^-(g)$ of $g$ isdefined as $gamma_{g}^-(g)=min{sum_{vin v(g)} f(v)mid fmbox{ is a global minus dominating function of } g}$. in thispaper we initiate the study of global minus domination number ingraphs and we establish lower and upper bounds for the globalminus domination number.