Inverse problem for Sturm-Liouville operators on hedgehog-type graphs (Q650443)

An inverse spectral problem is studied for second-order differential operators on hedgehog-type graphs with a cycle and with standard matching conditions in internal vertices. The inverse spectral problem for Sturm-Liouville operators on graphs without cycles was studied by the author [Inverse Probl. 21, No. 3, 1075--1086 (2005; Zbl 1089.34009)] and others. The presence of cycles in the graph structure requires serious modifications in the investigation. A uniqueness theorem is proved, and a constructive procedure for the solution is obtained.