Inversion diameter conjecture for graphs

Let $G$ be a graph, let $\mathcal{I}(G)$ be its inversion graph, and let $\Delta(G)$ denote its maximum degree. Inversion diameter conjecture. For every graph $G$,

$$\operatorname{diam}(\mathcal{I}(G)) \leqslant \Delta(G).$$

This would give a bound on inversion diameter solely in terms of maximum degree; the source does not provide a resolution.