An inverse spectral problem is studied for Sturm-Liouville differential operators on hedgehog-type graphs with generalized matching conditions in the interior vertices and with Dirichlet boundary conditions in the boundary vertices. A uniqueness theorem of recovering potentials from given spectral characteristics is provided, and a constructive solution for the inverse problem is obtained.
"An Inverse Problem for Differential Operators on Hedgehog-type Graphs with General Matching Conditions." Commun. Math. Anal. 17 (2) 98 - 107, 2014.