A counterexample to a conjecture of Jafari Rad and Volkmann

Abstract

In this short note, we disprove the conjecture of Jafari Rad and Volkmannthat every $\gamma $-vertex critical graph is $\gamma _{R}$-vertex critical,where $\gamma (G)$ and $\gamma _{R}(G)$ stand for the domination number andthe Roman domination number of a graph $G$, respectively.