References

  1. Ashurova E.N., Kandagura A.N., Karpenko I.I. The criterion of simplicity for symmetric operator on a graph, Methods Func. Anal. Topology 2014, 20 (2), 117-123.
  2. Belishev M.I., Vakulenko A.F. Inverse problems on graphs: recovering the tree of strings by the BC-method. J. Inverse Ill-Posed Probl. 2006, 14 (1), 29-46.
  3. Belishev M.I., Wada N. On revealing graph cycles via boundary measurements. Inverse Problems 2009, 25 (10), 105011, 21 pp.
  4. Berkolaiko G., Kuchment P. Introduction to Quantum Graphs. In: Mathematical Surveys and Monographs, 186. AMS, 2012.
  5. Derkach V.A., Malamud M.M. Generalized resolvents and the boundary value problems for Hermitian operators with gaps. J. Funct. Anal. 1991, 95, 1-95.
  6. Ershova Yu., Kiselev A.V. Trace formulae for graph Laplacians with applications to recovering matching conditions. Methods Funct. Anal. Topol. 2012, 18 (4), 343-359.
  7. Ershova Yu., Kiselev A.V. Trace formulae for Schrodinger operators on metric graphs with applications to recovering matching conditions. Methods Funct. Anal. Topol. 2014, 20 (2), 134-148.
  8. Ershova Yu., Karpenko I.I., Kiselev A.V. Isospectrality for graph Laplacians under the change of coupling at graph vertices. arXiv: 1405.2997 [math.sp]. To appear in: J. Spectr. Th.
  9. Ershova Yu., Karpenko I.I., Kiselev A.V. Isospectrality for graph Laplacians under the change of coupling at graph vertices: necessary and sufficient conditions. arXiv: 1405.5016 [math.sp]. To appear in: Mathematika (UCL).
  10. Exner P. A duality between Schrodinger operators on graphs and certain Jacobi matrices. Ann. Inst. H. Poincare 1997, 66, 359-371.
  11. Exner P. Lattice Kronig-Penney models. Phys. Rev. Lett. 1995, 74, 3503-3506.
  12. Gorbachuk V.I., Gorbachuk M.L. Boundary value problems for operator differential equations. [Translated and revised from the 1984 Russian original]. In: Mathematics and its Applications (Soviet Series), 48. Kluwer Academic Publishers Group, Dordrecht, 1991.
  13. Gutkin B., Smilansky U. Can one hear the shape of a graph?. J. Phys. A. 2001, 34, 6061-6068.
  14. Kostrykin V., Potthoff J., Schrader R. Heat kernels on metric graphs and a trace formula. In: "Adventures in Mathematical Physics", Contemporary Mathematics, 447. Amer. Math. Soc., 2007, 175-198.
  15. Kostrykin V., Schrader R. Kirchhoff's rule for quantum wires. J. Phys. A. 1999, 32, 595-630.
  16. Kottos T., Smilansky U. Periodic orbit theory and spectral statistics for quantum graphs. Ann. Physics 1999, 274, 76-124.
  17. Kocubei A.N. On extension of symmetric operators and symmetric binary relations. Math. Notes 1975, 17, 41-48.
  18. Kocubei A. N. Characteristic functions of symmetric operators and their extensions. Izv. Akad. Nauk Arm. SSR, Ser. Mat. 1980, 15, 3, 219-232. (in Russian)
  19. Kuchment P. Quantum graphs: an introduction and a brief survey. In: "Analysis on Graphs and its Applications", Proc. Symp. Pure. Math. AMS 2008, 291-314.
  20. Kurasov P., Nowaczyk M. Inverse spectral problem for quantum graphs. J. Phys. A: Mathematical and General 2005, 38, 4901-4915. correction: J. Phys. A: Mathematical and General 2006, 39, 993.
  21. Kurasov P. Graph Laplacians and Topology. Arkiv for Matematik 2008, 46, 95-111.
  22. Levin B.Ya. Lectures on entire functions. [In collaboration with and with a preface by Yu. Lyubarskii, M. Sodin and V. Tkachenko. Translated from the Russian manuscript by Tkachenko.] In: Translations of Mathematical Monographs, 150. American Mathematical Society, Providence, RI, 1996. xvi+248 pp.
  23. Pivovarchik V., Taystruk O. On characteristic functions of operators on equilateral graphs. Methods Funct. Anal. Topol. 2012, 18 (2), 189-197.
  24. Roth J.P. Le spectre du Laplacien sur un graphe. In: Theorie du Potentiel, Lect. Notes in Math., 1096. Orsay, 1983. 521-539.
  25. Tutte W. T. Graph theory. [With a foreword by C. St. J. A. Nash-Williams]. In: Encyclopedia of Mathematics and its Applications, 21. Addison-Wesley Publishing Company, Advanced Book Program, Reading, MA, 1984. xxi+333 pp.