  We present a Fermi golden rule giving rates of decay of states obtained by
perturbing embedded eigenvalues of a quantum graph. To illustrate the procedure
in a notationally simpler setting we also present a Fermi Golden Rule for
boundary value problems on surfaces with constant curvature cusps. We also
provide a resonance existence result which is uniform on compact sets of
energies and metric graphs. The results are illustrated by numerical
experiments.
