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This article has been retracted as it is essentially identical in content with the published article “Determination of Sturm-Liouville operator on a three-star graph from four spectra,” by I. Dehghani Tazehkand and A. Jodayree Akbarfam and published in Acta Universitatis Apulensis No. 32/2012, pp.147-172.

ISRN Applied Mathematics
Volume 2012 (2012), Article ID 132842, 23 pages
Research Article

An Inverse Spectral Problem for the Sturm-Liouville Operator on a Three-Star Graph

Faculty of Mathematical Sciences, University of Tabriz, 29 Bahman Boulevard, Tabriz, Iran

Received 10 January 2012; Accepted 15 March 2012

Academic Editor: D. Georges

Copyright © 2012 I. Dehghani Tazehkand and A. Jodayree Akbarfam. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


We study an inverse spectral problem for the Sturm-Liouville operator on a three-star graph with the Dirichlet and Robin boundary conditions in the boundary vertices and matching conditions in the internal vertex. As spectral characteristics,we consider the spectrum of the main problem together with the spectra of two Dirichlet-Dirichlet problems and one Robin-Dirichlet problem on the edges of the graph and investigate their properties and asymptotic behavior. We prove that if these four spectra do not intersect, then the inverse problem of recovering the operator is uniquely solvable.We give an algorithm for the solution of the inverse problem with respect to this quadruple of spectra.