Includes bibliographical references.

Nodal domains on graphs -- how to count them and why? / Ram Band, Idan Oren and Uzy Smilansky -- Zeta functions of weighted graphs and covering graphs / Matthew D. Horton, H. M. Stark and Audrey A. Terras -- Discrete geometric analysis / Toshikazu Sunada -- Uniform existence of the integrated density of states for combinatorial and metric graphs over $\mathbb {Z}^d$ / Michael J. Gruber, Daniel H. Lenz and Ivan Veseli�c -- Bartholdi zeta functions for periodic simple graphs / Daniele Guido, Tommaso Isola and Michel L. Lapidus -- Asymptotic properties of Markov processes on Cayley trees / M. Kelbert and Y. Suhov -- Groups and analysis on fractals / Volodymyr Nekrashevych and Alexander Teplyaev -- Schreier spectrum of the Hanoi Towers group on three pegs / Rostislav Grigorchuk and Zoran �Suni�c -- On the dichotomy in the heat kernel two sided estimates / Alexander Grigoryan and Takashi Kumagai -- Tube formulas for self-similar fractals / Michel L. Lapidus and Erin P. J. Pearse -- Existence of eigenforms on nicely separated fractals / Roberto Peirone -- Trace formulae for quantum graphs / Jens Bolte and Sebastian Endres -- Quantum graphs with spin Hamiltonians / J. M. Harrison -- Quantum graphs and quantum chaos / J. P. Keating -- Quantum graphs: An introduction and a brief survey / Peter Kuchment -- Two constructions of quantum graphs and two types of spectral statistics / G. Berkolaiko -- An example on the discrete spectrum of a star graph / B. M. Brown, M. S. P. Eastham and I. G. Wood -- The HELP inequality on trees / B. Malcolm Brown, Matthias Langer and Karl Michael Schmidt -- Boundary value problems for infinite metric graphs / Robert Carlson -- Remarks about Hardy inequalities on metric trees / Tomas Ekholm, Rupert L. Frank and Hynek Kova�r�ik -- On the spectral gap in Andreev graphs / Holger Flechsig and Sven Gnutzmann -- An inverse spectral problem for Sturm-Liouville operators with singular potentials on star-type graphs / G. Freiling, M. Ignatiev and V. Yurko -- Optimal Wegner estimates for random Schr�odinger operators on metric graphs / Michael J. Gruber, Mario Helm and Ivan Veseli�c -- Contraction semigroups on metric graphs / Vadim Kostrykin, J�urgen Potthoff and Robert Schrader -- Localization in a quasiperiodic model on quantum graphs / Konstantin Pankrashkin -- Equilateral quantum graphs and boundary triples / Olaf Post -- A conditionally convergent trace formula for quantum graphs / B. Winn -- Control problems on quantum graphs / Sergei Avdonin -- Leaky quantum graphs: A review / Pavel Exner -- Thin tubes in mathematical physics, global analysis and spectral geometry / Daniel Grieser -- Simulation of quantum graphs by microwave networks / Oleh Hul, Micha� �awniczak, Szymon Bauch and Leszek Sirko -- Twisting versus bending in quantum waveguides / David Krej�ci�r�ik -- Quantum field theory on star graphs / B. Bellazzini, M. Burrello, M. Mintchev and P. Sorba -- On the skeleton method and an application to a quantum scissor / H. D. Cornean, P. Duclos and B. Ricaud -- Vacuum energy and closed orbits in quantum graphs / S. A. Fulling and J. H. Wilson -- Spectra of graphs and semi-conducting polymers / Philipp Schapotschnikow and Sven Gnutzmann --

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Electronic reproduction. Providence, Rhode Island : American Mathematical Society. 2012

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