Extended results on restrained domination number and connectivity of a graph

A subset $S$ of $V$ is called a dominating set in $G$ if every vertex in $V-S$ is adjacent to at least one vertex in $S$. A dominating set $S$ is said to be a restrained dominating set if $langle V-S rangle$ contains no isolated vertices. The minimum cardinality of a restrained dominating set of $G$ is called the restrained domination number of $G$ and is denoted by $gamma_{r}(G)$. The connectivity $kappa(G)$ of a graph $G$ is the minimum number of vertices whose removal results in a disconnected or trivial graph. In this paper we characterized the graphs with sum of restrained domination number and connectivity is equal to $2n-6$.