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Boundary value problems on hedgehog-type graphs for Sturm-Liouvilledifferential operators with general matching conditions are studied. Weinvestigate inverse spectral problems of recovering the coefficients of thedifferential equation from the spectral data. For this inverse problem we provea uniqueness theorem and provide a procedure for constructing its solution.

Inverse Spectral Problems for Sturm-Liouville Operators on Hedgehog-type Graphs with General Matching Conditions