  We study the spectra of mixed graphs about its Hermitian adjacency matrix of
the second kind (i.e. N-matrix) introduced by Mohar [1]. We extend some results
and define one new Hermitian adjacency matrix, and the entry corresponding to
an arc from $u$ to $v$ is equal to the $k$-th( or the third) root of unity,
i.e. ${\omega} = cos(2{\pi}/k) + \textbf{i} \ sin(2{\pi}/k), k {\geq} 3$; the
entry corresponding to an undirected edge is equal to 1, and 0 otherwise. In
this paper, we characterize the cospectrality conditions for a mixed graph and
its underlying graph. In section 4, we determine a sharp upper bound on the
spectral radius of mixed graphs, and provide the corresponding extremal graphs.
