  We analyze spectral properties of a quantum graph in the form of a ring chain
with a $\delta$ coupling in the vertices exposed to a homogeneous magnetic
field perpendicular to the graph plane. We find the band spectrum in the case
when the chain exhibits a translational symmetry and study the discrete
spectrum in the gaps resulting from changing a finite number of vertex coupling
constants. In particular, we discuss in details some examples such as
perturbations of one or two vertices, weak perturbation asymptotics, and a pair
of distant perturbations.
