Inverse spectral problems for Sturm-Liouville operators on graphs

Sturm-Liouville differential operators on compact graphs without cycles (i.e. oil trees) are studied. We establish properties of the spectral characteristics and investigate two inverse problems of recovering the operator from the so-called WeyI functions and from a system of spectra. For these inverse problems, we prove the uniqueness theorems and obtain a procedure for constructing the solution by the method of spectral mappings.