On the Inverse Problem for Quantum Graphs with One Cycle |

P. Kurasov
Dept. of Mathematics, LTH, Lund Univ., Box 118, 221 00 Lund, Sweden Dept. of Mathematics, Stockholm Univ., 106 91, Stockholm, Sweden and Dept. of Physics, St. Petersburg Univ., 198904 St. Peterhof, Russia |

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Quantum graphs having one cycle are considered. It is shown that if the cycle contains at least three vertices, then the potential on the graph can be uniquely reconstructed from the corresponding Titchmarsh-Weyl function (Dirichlet to Neumann map) associated with graph's boundary, provided certain non resonant conditions are satisfied. |

DOI: 10.12693/APhysPolA.116.765 PACS numbers: 03.65.Nk, 73.63.-b, 85.35.-p |