  Let $ G $ be a simple graph of $ \ell $ vertices $ \{1, \dots, \ell \} $ with
edge set $ E_{G} $. The graphical arrangement $ \mathcal{A}_{G} $ consists of
hyperplanes $ \{x_{i}-x_{j}=0\} $, where $ \{i, j \} \in E_{G} $. It is well
known that three properties, chordality of $ G $, supersolvability of $
\mathcal{A}_{G} $, and freeness of $ \mathcal{A}_{G} $ are equivalent.
Recently, Richard P. Stanley introduced $ \psi $-graphical arrangement $
\mathcal{A}_{G, \psi} $ as a generalization of graphical arrangements. Lili Mu
and Stanley characterized the supersolvability of the $ \psi $-graphical
arrangements and conjectured that the freeness and the supersolvability of $
\psi $-graphical arrangements are equivalent. In this paper, we will prove the
conjecture.
