If atoms in star A and star B are moving in opposition - away and towards one other in a steady-state oscillation - this would cause destructive interference between the emitted photons. No energy will be exchanged and they will be blind to one another.
If the atoms of stars A and C are moving back and forth synchronously in the same direction at the same time, the photons they emit will add constructively and they will see one another.
If you want to, you can make stars A and C stationary and just let star B vibrate. The result is the same.