On the Spectral Gap for Networks of Beams

A notion of standard vertex conditions for beam operarators (the fourth derivative) on metric graphs is presented, and the spectral gap (the difference between the first two eigenvalues) for the operator with these conditions is studied. Upper and lower estimates for the spectral gap are obtained, and it is shown that stronger estimates can be obtained for certain classes of graphs. Graph surgery is used as a technique for estimation. A geometric version of the Ambartsumian theorem for networks of beams is proved.