The hypoenergeticity conjecture for group-annihilator graphs of cyclic prime-power groups

Let $p$ be a prime and let $\alpha$ be a positive integer. Consider the group-annihilator graph realised by the group $\mathbb{Z}/p^{\alpha}\mathbb{Z}$. Hypoenergeticity conjecture. For any positive integer $\alpha$, this graph is not hyperenergetic but hypoenergetic. This conjecture extends the preceding result for $\alpha=2$ to all positive integers and concerns the energy of threshold graphs arising from finite abelian groups.