About noncommuting graphs

The noncommuting $\nabla(G)$ of a nonabelian finite group $G$ is defined as follows: The vertices of $\nabla(G)$ are represented by the noncentral elements of $G$, and two distinct vertices $x$ and $y$ are joined by an edge if $xy\ne yx$. In [1], the following was conjectured: Let $G$ and $H$ be two nonabelian finite groups such that $\nabla(G)\cong\nabla(H)$ then $|G|=|H|$. Here we give some counterexamples to this conjecture.