RESTRICTED MINUS DOMINATION NUMBER OF A GRAPH

A restricted minus dominating function on a graph $G=(V, E)$ is a function $f:V\rightarrow\{-1, 0, 1\}$ such that $f(N[v])\geq 0$ for every vertex $v\in V$ and a vertex assigned 0 is adjacent to at least one vertex assigned 1. The restricted minus domination number $\gamma_{r}^{-}(G)=min\{w(f):f$ is restricted minus dominating function$\}$. In this paper, we initiate the study of $\gamma_{r}^{-}(G)$ and its relationship with sign and minus domination are investigated. Many of the known bounds of $\gamma_{r}^{-}(G)$ are immediate consequence of our results.