Elphick–Wocjan conjecture on positive and negative p-energies

Let $G$ be a connected graph with $n$ vertices, and let $\mathcal{E}_p^+(G)$ and $\mathcal{E}_p^-(G)$ denote its positive and negative $p$-energies. Elphick–Wocjan conjecture. For $0\leq pleq 2$,

$$\min\left\{\mathcal{E}_p^+(G),\mathcal{E}_p^-(G)\right\}\geq (n-1)^{p/2}.$$

The conjecture is proposed as a $p$-energy analogue of a conjecture of Elphick, Wocjan, Farber, and Goldberg. Its status is not specified in the supplied text.