Abdollahi–Akbari–Maimani order conjecture for non-commuting graphs

Let $G$ and $H$ be non-abelian finite groups. For a finite non-abelian group $K$, let $\Gamma_K$ be the graph whose vertices are the non-central elements of $K$, with two vertices adjacent when they do not commute. Abdollahi–Akbari–Maimani order conjecture. If

$$\Gamma_G\cong\Gamma_H,$$

then

$$|G|=|H|.$$

The conjecture concerns whether the non-commuting graph determines the order of a finite group. It is known for $p$-groups, dihedral groups, and simple groups, but remains open in general; the source also notes that it suffices to establish it for finite AC-groups.