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) (271, Yurko (2009) [28]) we show that (1) if the potential function q(j)(x) on a fixed edge e(j) is prescribed on the interval [pi/2, pi]. then the reciprocal of d of the spectrum suffices to determine q(j)(x) on the whole interval [0, pi]; (2) the 2 over d of the spectrum suffices to determine q(j)(x) on a fixed edge e(j). (C) 2009 Elsevier Inc. All rights reserved.