Ebrahimi–Mohar–Nikiforov–Ahmady conjecture on the spectral sum of graphs

Let $G$ be any graph of order $n$, and let $\lambda_1(G)$ and $\lambda_2(G)$ denote its two largest adjacency eigenvalues. Ebrahimi–Mohar–Nikiforov–Ahmady conjecture. The spectral sum satisfies

$$\lambda_1(G)+\lambda_2(G)\leq \frac{8n}{7}.$$

The conjecture extends the extremal spectral-sum question from trees to arbitrary graphs. The supplied context states that analogous questions for graphs remain open and gives no resolution of this bound.