  For an oriented graph $D$, the $inversion$ of $X \subseteq V(D)$ in $D$ is
the digraph obtained from $D$ by reversing the direction of all arcs with both
ends in $X$. The inversion number of $D$, denoted by $inv(D)$, is the minimum
number of inversions needed to transform $D$ into an acyclic digraph. In this
paper, we first show that $inv (\overrightarrow{C_3} \Rightarrow D)= inv(D) +1$
for any oriented graph $\textit{D}$ with even inversion number $inv(D)$, where
the dijoin $\overrightarrow{C_3} \Rightarrow D$ is the oriented graph obtained
from the disjoint union of $\overrightarrow{C_3}$ and $D$ by adding all arcs
from $\overrightarrow{C_3}$ to $D$. Thus we disprove the conjecture of Aubian
el at. \cite{2212.09188} and the conjecture of Alon el at. \cite{2212.11969}.
We also study the blow-up graph which is an oriented graph obtained from a
tournament by replacing all vertices into oriented graphs. We construct a
tournament $T$ with order $n$ and $inv(T)=\frac{n}{3}+1$ using blow-up graphs.
