Certified domination number in corona product of graphs

Abstract

A set $S$ of vertices in $G=(V, E)$ is called a dominating set of $G$ if every vertex not in $S$ has at least one neighbour in $S$. A dominating set $S$ of a graph $G$ is said to be a certified dominating set of $G$ if every vertex in $S$ has either zero or at least two neighbours in $V \backslash S$. The certified domination number, $\gamma_{c e r}(G)$ of $G$ is defined as the minimum cardinality of certified dominating set of $G$. In this paper, we study the certified domination number of Corona product of some standard graphs.