Author/Authors :
عطاپور، مريم نويسنده Department of Mathematics, University of Bonab, Bonab Atapour, Maryam , نوروزيان، سپيده نويسنده Department of Mathematics, Azarbaijan Shahid Madani University, Tabriz Norouzian, Sepideh , شيخ الاسلامي، سيد محمد نويسنده Department of Mathematics, Azarbaijan Shahid Madani University, Tabriz, I.R. Iran Sheikholeslami, S. M.
Abstract :
A function $f:V(G)rightarrow {-1,0,1}$ is a {em 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 {em global minus dominating function} if $f$ is also a minus
dominating function of the complement $overline{G}$ of $G$. The
{em global minus domination number} $gamma_{g}^-(G)$ of $G$ is
defined as $gamma_{g}^-(G)=min{sum_{vin V(G)} f(v)mid f
mbox{ is a global minus dominating function of } G}$. In this
paper we initiate the study of global minus domination number in
graphs and we establish lower and upper bounds for the global
minus domination number.
