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The noncommuting graph $\nabla(G)$ of a nonabelian finite group
$G$ is defined as follows: The vertices of $\nabla(G)$ are
represented by the non-central elements of $G$, and two distinct
vertices $x$ and $y$ are joined by an edge if $xy\neq yx$. In [2],
it was conjectured that: Let $G$ and $H$ be two nonabelian finite
groups such that $\nabla(G)\cong \nabla(H)$, then $|G|=|H|$. In
this article we give, some counterexamples to this conjecture.
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