Mostar index extremal graph conjecture

For a connected simple graph $G$, let $\mathrm{Mo}(G)$ denote its Mostar index. For graphs $G_1$ and $G_2$, let $G_1 \lor G_2$ denote their join. Write $K_r$ for the complete graph on $r$ vertices, $\overline{K_r}$ for the edgeless graph on $r$ vertices, and let $n$ be the order of a graph.

Mostar index extremal graph conjecture. For any $n \ge 3$, the graph

$$K_{\lfloor n / 3 \rfloor} \lor \overline{K_{\lceil 2n / 3 \rceil}}$$

attains the maximum Mostar index among all connected simple graphs of order $n$.

The conjecture concerns the extremal structure of the Mostar index and was described in the source as still open. The index was introduced by Došlić et al. and independently discovered by Sharafdini and Réti.