  Let $G$ be a connected graph and let $T$ be a spanning tree of $G$. A partial
orientation $\sigma$ of $G$ respect to $T$ is an orientation of the edges of
$G$ except those edges of $T$, the resulting graph associated with which is
denoted by $G_T^\sigma$. In this paper we prove that there exists a partial
orientation $\sigma$ of $G$ respect to $T$ such that the largest eigenvalue of
the Hermitian adjacency matrix of $G_T^\sigma$ is at most the largest absolute
value of the roots of the matching polynomial of $G$.
