F. [. Albeverio, R. Gesztesy, H. Høegh-krohn, and . Holden, Solvable Models in Quantum Mechanics, 2005.

T. Cheon and P. Exner, An approximation to ???? couplings on graphs, Journal of Physics A: Mathematical and General, vol.37, issue.29, pp.329-335, 2004.
DOI : 10.1088/0305-4470/37/29/L01

T. Cheon and T. Shigehara, Realizing discontinuous wave functions with renormalized short-range potentials, Physics Letters A, vol.243, issue.3, pp.243-111, 1998.
DOI : 10.1016/S0375-9601(98)00188-1

P. Exner, J. P. Keating, P. Kuchment, T. Sunada, and A. Teplyaev, Analysis on Graphs and Applications, Proceedings of a Isaac Newton Institute programme AMS " Proceedings of Symposia in Pure Mathematics " Series, 2007.

P. Exner, H. Neidhardt, and V. A. , Potential Approximations to ??': An Inverse Klauder Phenomenon with Norm-Resolvent Convergence, Communications in Mathematical Physics, vol.224, issue.3, pp.593-612, 2001.
DOI : 10.1007/s002200100567

P. Exner and O. Post, Approximation of quantum graph vertex couplings by scaled Schrödinger operators on thin branched manifolds

P. Exner and P. ?eba, Free quantum motion on a branching graph, Reports on Mathematical Physics, vol.28, issue.1, pp.7-26, 1989.
DOI : 10.1016/0034-4877(89)90023-2

P. Exner and O. Turek, APPROXIMATIONS OF SINGULAR VERTEX COUPLINGS IN QUANTUM GRAPHS, Reviews in Mathematical Physics, vol.19, issue.06, pp.571-606, 2007.
DOI : 10.1142/S0129055X07003073

T. Fül?-op and I. Tsutsui, A free particle on a circle with point interaction, pp.366-374, 2000.

V. I. Gorbachuk and M. L. Gorbachuk, Boundary value problems for operato differential equations, 1991.

M. Harmer, Hermitian symplectic geometry and extension theory, Journal of Physics A: Mathematical and General, vol.33, issue.50, pp.9193-9203, 2000.
DOI : 10.1088/0305-4470/33/50/305

V. Kostrykin and R. Schrader, Kirchhoff's rule for quantum wires, Journal of Physics A: Mathematical and General, vol.32, issue.4, pp.595-630, 1999.
DOI : 10.1088/0305-4470/32/4/006

V. Kostrykin and R. Schrader, Kirchhoff's Rule for Quantum Wires. II: The Inverse Problem with Possible Applications to Quantum Computers, Fortschritte der Physik, vol.48, issue.8, pp.703-716, 2000.
DOI : 10.1002/1521-3978(200008)48:8<703::AID-PROP703>3.0.CO;2-O

P. Kuchment, Quantum graphs: I. Some basic structures, Waves in Random Media, vol.14, issue.1, pp.107-128, 2004.
DOI : 10.1088/0959-7174/14/1/014

K. Ruedenberg and C. W. Scherr, Free???Electron Network Model for Conjugated Systems. I. Theory, The Journal of Chemical Physics, vol.21, issue.9, pp.1565-1581, 1953.
DOI : 10.1063/1.1699299

T. Shigehara, H. Mizoguchi, T. Mishima, and T. Cheon, Realization of a four parameter family of generalized one-dimensional contact interactions by three nearby delta potentials with renormalized strengths, IEICE Trans. Fund. Elec. Comm. Comp. Sci, pp.82-1708, 1999.

K. Ruedenberg and C. W. Scherr, Free???Electron Network Model for Conjugated Systems. I. Theory, The Journal of Chemical Physics, vol.21, issue.9, pp.1565-1581, 1953.
DOI : 10.1063/1.1699299

N. I. Gerasimenko and B. S. Pavlov, Scattering problems on noncompact graphs, Theoretical and Mathematical Physics, vol.73, issue.3, pp.345-359, 1988.
DOI : 10.1007/BF01016616

P. Exner and P. Seba, Free quantum motion on a branching graph, Reports on Mathematical Physics, vol.28, issue.1, pp.7-26, 1989.
DOI : 10.1016/0034-4877(89)90023-2

S. Albeverio, F. Gesztesy, R. Høegh-krohn, and H. Holden, Solvable Models in Quantum Mechanics, 2005.

P. Kuchment, Quantum graphs: I. Some basic structures, Waves in Random Media, vol.14, issue.1, pp.107-128, 2004.
DOI : 10.1088/0959-7174/14/1/014

M. Freidlin and A. Wentzell, Diffusion Processes on Graphs and the Averaging Principle, The Annals of Probability, vol.21, issue.4, pp.2215-2245, 1993.
DOI : 10.1214/aop/1176989018

P. Kuchment and H. Zeng, Convergence of Spectra of Mesoscopic Systems Collapsing onto a Graph, Journal of Mathematical Analysis and Applications, vol.258, issue.2, pp.671-700, 2001.
DOI : 10.1006/jmaa.2000.7415

J. Rubinstein and M. Schatzmann, Variational Problems??on Multiply Connected Thin Strips I:??Basic Estimates and Convergence??of the Laplacian Spectrum, Archive for Rational Mechanics and Analysis, vol.160, issue.4, pp.271-308, 2001.
DOI : 10.1007/s002050100164

T. Saito, Convergence of the Neumann Laplacian on shrinking domains, Analysis, vol.21, issue.2, pp.171-204, 2001.
DOI : 10.1524/anly.2001.21.2.171

P. Exner and O. Post, Convergence of spectra of graph-like thin manifolds, Journal of Geometry and Physics, vol.54, issue.1, pp.77-115, 2005.
DOI : 10.1016/j.geomphys.2004.08.003

O. Post, Spectral convergence of non-compact quasi-one-dimensional spaces, pp.933-973, 2006.

O. Post, Branched quantum wave guides with Dirichlet boundary conditions: the decoupling case, Journal of Physics A: Mathematical and General, vol.38, issue.22, pp.4917-4931, 2005.
DOI : 10.1088/0305-4470/38/22/015

S. Molchanov and B. Vainberg, Scattering Solutions in Networks of Thin Fibers: Small Diameter Asymptotics, Communications in Mathematical Physics, vol.30, issue.2, p.609021
DOI : 10.1007/s00220-007-0220-8

P. Exner, Weakly coupled states on branching graphs, Letters in Mathematical Physics, vol.22, issue.3, pp.313-320, 1996.
DOI : 10.1007/BF00398355

T. Cheon and T. Shigehara, Realizing discontinuous wave functions with renormalized short-range potentials, Physics Letters A, vol.243, issue.3, pp.111-116, 1998.
DOI : 10.1016/S0375-9601(98)00188-1
URL : http://arxiv.org/abs/quant-ph/9709035

S. Albeverio and L. Nizhnik, Approximation of general zero-range potentials, Ukrainian Math, J, vol.52, pp.582-589, 2000.

P. Exner, H. Neidhardt, and V. A. Zagrebnov, Potential Approximations to ??': An Inverse Klauder Phenomenon with Norm-Resolvent Convergence, Communications in Mathematical Physics, vol.224, issue.3, pp.593-612, 2001.
DOI : 10.1007/s002200100567

T. Cheon and P. Exner, An approximation to ???? couplings on graphs, Journal of Physics A: Mathematical and General, vol.37, issue.29, pp.329-335, 2004.
DOI : 10.1088/0305-4470/37/29/L01

P. Exner, O. Turek, and G. Berkolaiko, Approximations of permutation-symmetric vertex couplings in quantum graphs, Contemporary Mathematics, vol.415, pp.109-120, 2006.
DOI : 10.1090/conm/415/07863

J. E. Avron, P. Exner, and Y. Last, Periodic Schr??dinger operators with large gaps and Wannier-Stark ladders, Physical Review Letters, vol.72, issue.6, pp.896-899, 1994.
DOI : 10.1103/PhysRevLett.72.896

V. Kostrykin and R. Schrader, Kirchhoff's rule for quantum wires, Journal of Physics A: Mathematical and General, vol.32, issue.4, pp.595-630, 1999.
DOI : 10.1088/0305-4470/32/4/006

M. Harmer, Hermitian symplectic geometry and extension theory, Journal of Physics A: Mathematical and General, vol.33, issue.50, pp.9193-9203, 2000.
DOI : 10.1088/0305-4470/33/50/305
URL : http://arxiv.org/abs/math-ph/0703027

P. Exner, Lattice Kronig-Penney Models, Physical Review Letters, vol.74, issue.18, pp.3503-3506, 1995.
DOI : 10.1103/PhysRevLett.74.3503

P. Exner, Contact interactions on graph superlattices, Journal of Physics A: Mathematical and General, vol.29, issue.1, pp.87-102, 1996.
DOI : 10.1088/0305-4470/29/1/011

V. Kostrykin and R. Schrader, Kirchhoff's rule for quantum wires, Journal of Physics A: Mathematical and General, vol.32, issue.4, pp.595-630, 1999.
DOI : 10.1088/0305-4470/32/4/006

I. Tsutsui, T. Fülöp, and T. Cheon, M??bius structure of the spectral space of Schr??dinger operators with point interaction, Journal of Mathematical Physics, vol.42, issue.12, pp.5687-5697, 2001.
DOI : 10.1063/1.1415432

P. Exner, Contact interactions on graph superlattices, Journal of Physics A: Mathematical and General, vol.29, issue.1, pp.87-102, 1996.
DOI : 10.1088/0305-4470/29/1/011

T. Cheon and T. Shigehara, Realizing discontinuous wave functions with renormalized short-range potentials, Physics Letters A, vol.243, issue.3, pp.111-116, 1998.
DOI : 10.1016/S0375-9601(98)00188-1

P. Exner and O. Turek, APPROXIMATIONS OF SINGULAR VERTEX COUPLINGS IN QUANTUM GRAPHS, Reviews in Mathematical Physics, vol.19, issue.06, pp.571-606, 2007.
DOI : 10.1142/S0129055X07003073

. References, M. Aizenman, and J. Schenker, The creation of spectral gaps by graph decorations Lett, Math. Phys, vol.53, pp.253-62, 2000.

C. Cacciapuoti and P. Exner, Nontrivial edge coupling from a Dirichlet network squeezing: the case of a bent waveguide, Journal of Physics A: Mathematical and Theoretical, vol.40, issue.26, pp.40-511, 2007.
DOI : 10.1088/1751-8113/40/26/F02

P. Duclos and P. Exner, Curvature-induced bound states in quantum waveguides in two and three dimensions Rev, Math. Phys, vol.7, pp.73-102, 1995.

P. Exner and P. , Free quantum motion on a branching graph Rep, Math. Phys, vol.28, pp.7-26, 1989.

P. Kuchment, Quantum graphs: II. Some spectral properties of quantum and combinatorial graphs, Journal of Physics A: Mathematical and General, vol.38, issue.22, pp.4887-900, 2005.
DOI : 10.1088/0305-4470/38/22/013

P. Kuchment and B. Vainberg, On the Structure of Eigenfunctions Corresponding to Embedded Eigenvalues of Locally Perturbed Periodic Graph Operators, Communications in Mathematical Physics, vol.33, issue.3, pp.673-86, 2006.
DOI : 10.1007/s00220-006-0105-2

K. Ruedenberg and C. W. Scherr, Free???Electron Network Model for Conjugated Systems. I. Theory, The Journal of Chemical Physics, vol.21, issue.9, pp.1565-81, 1953.
DOI : 10.1063/1.1699299