Star graphs and Seba billiards

We derive an exact expression for the two-point correlation function for qu antum star graphs in the limit as the number of bonds tends to infinity. Th is turns out to be identical to the corresponding result for certain Seba b illiards in the semiclassical limit. The reasons for this are discussed. Th e formula we derive is also shown to be equivalent to a series expansion fo r the form factor-the Fourier transform of the two-point correlation functi on-previously calculated using periodic orbit theory.