Tang–Liu–Wang positive p-energy conjecture

For a graph $G$, define its positive adjacency $p$-energy by

$$\mathcal E_p^+(G)=\sum_{\lambda_i(G)>0}\lambda_i(G)^p.$$

Let $p\ge2$ be a real number, and let $G$ be a connected graph with $n$ vertices. Tang–Liu–Wang's positive $p$-energy conjecture.

$$\mathcal E_p^+(G)\ge \mathcal E_p^+(P_n).$$

The conjecture asserts that among connected graphs on $n$ vertices, the path $P_n$ minimizes positive adjacency $p$-energy. Positive and negative $p$-energies arise in spectral graph theory and have applications to chromatic and related graph parameters; the source does not report a resolution of this conjecture.