  We discuss some simple H\"uckel-like matrix representations of non-Hermitian
operators with antiunitary symmetries that include generalized $\mathcal{PT}$
(parity transformation followed by time-reversal) symmetry. One of them
exhibits extremely broken antiunitary symmetry (complex eigenvalues for all
nontrivial values of the model parameter) because of the degeneracy of the
operator in the Hermitian limit. These examples illustrate the effect of
point-group symmetry on the spectrum of the non-Hermitian operators. We
construct the necessary unitary matrices by means of simple graphical
representations of the non-Hermitian operators.

Quantum Physics