On Restrained Domination Number of Graphs

Abstract

For a graph $G=(V,E)$, a set $S \subseteq V$ is a restrained dominating set if every vertex not in $S$ is adjacent to a vertex in $S$ and to a vertex in $V-S$. The smallest cardinality of a restrained dominating set of $G$ is called restrained domination number of $G$, denoted by $\gamma_r (G)$. We investigate restrained domination number of some cycle related graphs which are obtained by means of various graph operations on cycle.