  In an oriented graph $\overrightarrow{G}$, the inversion of a subset $X$ of
vertices consists in reversing the orientation of all arcs with both
end-vertices in $X$. The inversion graph of a graph $G$, denoted by
$\mathcal{I}(G)$, is the graph whose vertices are orientations of $G$ in which
two orientations $\overrightarrow{G_1}$ and $\overrightarrow{G_2}$ are adjacent
if and only if there is an inversion $X$ transforming $\overrightarrow{G_1}$
into $\overrightarrow{G_2}$. The inversion diameter of a graph $G$ is the
diameter of its inversion graph $\mathcal{I}(G)$ denoted by
$diam(\mathcal{I}(G))$. Havet, H\"orsch, and Rambaud~(2024) first proved that
for $G$ of treewidth $k$, $diam(\mathcal{I}(G)) \le 2k$, and there are graphs
of treewidth $k$ with inversion diameter $k+2$. In this paper, we construct
graphs of treewidth $k$ with inversion diameter $2k$, which implies that the
previous upper bound $diam(\mathcal{I}(G)) \le 2k$ is tight. Moreover, for
graphs with maximum degree $\Delta$, Havet, H\"orsch, and Rambaud~(2024) proved
$diam(\mathcal{I}(G)) \le 2\Delta-1$ and conjectured that $diam(\mathcal{I}(G))
\le \Delta$. We prove the conjecture when $\Delta=3$ with the help of computer
calculations.
