Inverse spectral problems for the Sturm–Liouville operator on a d-star graph

In this work, we consider inverse spectral problems for the Sturm–Liouville differential operator on a d-star-type graph with standard matching conditions in the internal vertex, where the integer d⩾2. By using the Yurko's method (Yurko (2008) [27], , Yurko (2009) [28]) we show that(1)if the potential function qj(x) on a fixed edge ej is prescribed on the interval , then the reciprocal of d of the spectrum suffices to determine qj(x) on the whole interval [0,π];(2)the 2 over d of the spectrum suffices to determine qj(x) on a fixed edge ej.