The Abdollahi–Akbari–Maimani non-commuting graph conjecture

Let $G$ be a group and let $Z(G)$ be its centre. Define the non-commuting graph $\triangledown(G)$ to have vertex set $G\setminus Z(G)$, with distinct vertices $x$ and $y$ adjacent exactly when $xy\ne yx$. Let $S$ be a non-abelian simple group.

Abdollahi–Akbari–Maimani conjecture. If

$$\triangledown(G)=\triangledown(S),$$

then

$$G\cong S.$$

The source states that the Thompson conjecture has been proved and consequently the AAM conjecture is correct, so this conjecture is solved.