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 Yurkoʹs method (Yurko (2008) [27], Yurko (2009) [28]) we show that(1) potential function q j ( x ) on a fixed edge e j is prescribed on the interval [ π 2 , π ] , then the reciprocal of d of the spectrum suffices to determine q j ( x ) on the whole interval [ 0 , π ] ; over d of the spectrum suffices to determine q j ( x ) on a fixed edge e j .