strength based domination in graphs

Let $g=(v,e)$ be a connected graph. let $asubseteq v$ and $vin v-a.$ the dominating strength of $a$ on $v$ is defined by $s(v,a)=sumlimits_{uin a}frac{1}{d(u,v)}.$ a subset $d$ of $v$ is called a strength based dominating set if for every vertex $vnotin d,$ there exists a subset $a$ of $d$ such that $s(v,a)geq 1.$ the $sb$-domination number $gamma_{sb}(g)$ is the minimum cardinality of a strength based dominating set of $g.$ in this paper we initiate a study of this parameter and indicate directions for further research.