Extended results on restrained domination number and connectivity of a graph

C Sivagnanam, M P Kulandaivel


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 $2n-6$.

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