an inverse triple effect domination in graphs

In this paper, an inverse triple effect domination is introduced for any finite graph $g=(v, e)$ simple and undirected without isolated vertices. a subset $d^{-1}$ of $v-d$ is an inverse triple effect dominating set if every $v in d^{-1}$ dominates exactly three vertices of $v-d^{-1}$. the inverse triple effect domination number $gamma_{t e}^{-1}(g)$ is the minimum cardinality over all inverse triple effect dominating sets in $g$. some results and properties on $gamma_{t e}^{-1}(g)$ are given and proved. under any conditions the graph satisfies $gamma_{t e}(g)+gamma_{t e}^{-1}(g)=n$ is studied. lower and upper bounds for the size of a graph that has $gamma_{t e}^{-1}(g)$ are putted in two cases when $d^{-1}=v-d$ and when $d^{-1} neq v-d .$ which properties of a vertex to be belongs to $d^{-1}$ or out of it are discussed. then, $gamma_{t e}^{-1}(g)$ is evaluated and proved for several graphs.