S. Akbari, H. Kumar, and B. Mohar's negative $p$-energy conjecture

Let $n$ and $p$ be positive integers with $p\geq 2$, let $G$ be a connected graph on $n$ vertices, and let $K_n$ denote the complete graph on $n$ vertices. Akbari–Kumar–Mohar's negative $p$-energy conjecture.

$$\mathcal{E}_p^-(G)\geq \mathcal{E}_p^-(K_n).$$

The source states that the conjecture was known for $p\geq 4$ and that this paper proves it for every integer $p\geq 3$; consequently, the remaining case $p=2$ is still open.