**Preprints**

- Quantum Graphs via Exercises

R. Band, S. Gnutzmann

arXiv:1711.07435 **Quotients of finite-dimensional operators by symmetry representations**

R. Band, G. Berkolaiko, C. H. Joyner, W. Liu

arXiv:1711.00918**Nodal Statistics on Quantum Graphs**

L. Alon, R. Band, G. Berkolaiko

arXiv:1709.10413**Ground state property of Neumann domains on the torus**

R. Band, S. Egger, A. J. Taylor

arXiv:1707.03488**Nonlinear Sturm Oscillation: from the interval to a star**

R. Band, A. J. Krueger

arXiv:1610.07068**Lyndon word decompositions and pseudo orbits on q-nary graphs**

R. Band, J. M. Harrison, M. Sepansky

arXiv:1610.03808

**Published or in press**

**Quantum graphs which optimize the spectral gap**

R. Band, G. Lévy

Annales Henri Poincaré, Volume 18 (2017), p. 3269-3323.**Courant-sharp Eigenvalues of Neumann 2-Rep-tiles**

R. Band, M. Bersudsky, D. Fajman

Letters in Mathematical Physics. , Volume 107 (2017) p. 821-859.**Universality of the frequency spectrum of laminates**

G. Shmuel, R. Band,

Journal of the Mechanics and Physics of Solids 92 (2016) p. 127.**Topological Properties of Neumann Domains**

R. Band, D. Fajman,

Annales Henri Poincaré, Volume 17, Issue 9 (2016) p. 2379.**Anomalous nodal count and singularities in the dispersion relation of honeycomb graphs**

R. Band, G. Berkolaiko, T. Weyand,

J. Math. Phys. 56 (2015) p. 122111. Chosen as Featured Article of the issue.**The Nodal Count {0,1,2,3,…} Implies the Graph is a Tree**

R. Band,

Phil. Trans. R. Soc. A 28 vol. 372 no. 2007 (2014) p. 20120504.**Universality of the momentum band density of periodic networks**

R. Band, G. Berkolaiko,

Phys. Rev. Lett. 111 (2013) p. 130404. Chosen as Editor’s selection.**Finite pseudo orbit expansions for spectral quantities of quantum graphs**

R. Band, J. M. Harrison, C. H. Joyner,

J. Phys. A: Math. Theor. 45 (2012) p. 325204.**Isospectral graphs with identical nodal counts**

I. Oren, R. Band,

J. Phys. A: Math. Theor. 45 (2012) p. 135203.**Nodal domains of a non-separable problem – the right angled isosceles triangle**

A. Aronovitch, R. Band, D. Fajman, S. Gnutzmann,

J. Phys. A: Math. Theor. 45 (2012) p. 085209. Featured article of the issue.**The Number of Nodal Domains on Quantum Graphs as a Stability Index of Graph Partitions**

R. Band, G. Berkolaiko, H. Raz, U. Smilansky,

Communications in Mathematical Physics 311 (2012) p. 815.**Note on the Role of Symmetry in Scattering from Isospectral Graphs and Drums**

R. Band, A. Sawicki, U. Smilansky,

Acta Physica Polonica A, Vol. 120 (2011), Proceedings of the 5th Workshop on Quantum Chaos and Localisation Phenomena.**Dynamics of Nodal Points and the Nodal Count on a Family of Quantum Graphs**

R. Band, G. Berkolaiko, U. Smilansky,

Annales Henri Poincaré 13 (2011) p. 145.**Scattering from isospectral quantum graphs**

R. Band, A. Sawicki, U. Smilansky,

J. Phys. A: Math. Theor. 43 (2010) p. 415201.**Linear Representations and Isospectrality with Boundary Conditions**

O. Parzanchevski, R. Band,

Journal of Geometric Analysis 20, 2 (2010) p. 439-471.**The Isospectral Fruits of Representation Theory: Quantum Graphs and Drums**

R. Band, O. Parzanchevski, G. Ben-Shach,

J. Phys. A: Math. Theor. 42 (2009) p. 175202. Best paper prize of the Journal of Physics A’.**Nodal domains on graphs – how to count them and why?**

R. Band, I. Oren, U. Smilansky,

Analysis on Graphs and its applications Proc. Symp. Pure Math. (Providence, RI: American Mathematical Society) (2008) p. 5-28.**Resolving the isospectrality of the dihedral graphs by counting nodal domains**

R. Band, U. Smilansky,

Eur. Phys. J. Special Topics 145 (2007) p. 171-179.**Nodal domains on isospectral quantum graphs: the resolution of isospectrality**

R. Band, T. Shapira, U. Smilansky,

J. Phys. A: Math. Gen. 39 (2006) p. 13999-14014.

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