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A Frucht Theorem for Quantum Graphs

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Book cover Spectral Theory, Mathematical System Theory, Evolution Equations, Differential and Difference Equations

Part of the book series: Operator Theory: Advances and Applications ((OT,volume 221))

Abstract

A celebrated theorem due to R.F rucht states that, roughly speaking, each group is abstractly isomorphic to the symmetry group of some graph. By “symmetry group” the group of all graph automorphisms is meant. We provide an analogue of this result for quantum graphs, i.e., for Schrödinger equations on a metric graph, after suitably defining the notion of symmetry.

Mathematics Subject Classification (2000). Primary 05C25; Secondary 35B06, 81Q35.

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Author information

Authors and Affiliations

  1. Institut für Analysis, Universität Ulm, Helmholtzstraße 18, D-89081, Ulm, Germany

    Delio Mugnolo

Authors
  1. Delio Mugnolo
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Correspondence to Delio Mugnolo .

Editor information

Editors and Affiliations

  1. , Abt. Mathematik V, Universität Ulm, Ulm, 89069, Germany

    Wolfgang Arendt

  2. Department of Mathematics, Virginia Polytechnic Institute, McBryde Hall 524, Blacksburg, 24061, Virginia, USA

    Joseph A. Ball

  3. Institut für Mathematik, AG Modellierung, Numerik und, TU Berlin, Straße des 17 Juni 136, Berlin, 10623, Berlin, Germany

    Jussi Behrndt

  4. Fak. II Mathematik & Naturwissenschaften, Institut für Mathematik, TU Berlin, Straße des 17. Juni 136, Berlin, 10623, Berlin, Germany

    Karl-Heinz Förster

  5. Fak. II Mathematik & Naturwissenschaften, Institut für Mathematik, TU Berlin, Straße des 17. Juni 136, Berlin, 10623, Berlin, Germany

    Volker Mehrmann

  6. , Institut für Mathematik, TU Ilmenau, Weimarer Str. 25, Ilmenau, 98693, Thüringen, Germany

    Carsten Trunk

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Mugnolo, D. (2012). A Frucht Theorem for Quantum Graphs. In: Arendt, W., Ball, J., Behrndt, J., Förster, KH., Mehrmann, V., Trunk, C. (eds) Spectral Theory, Mathematical System Theory, Evolution Equations, Differential and Difference Equations. Operator Theory: Advances and Applications, vol 221. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-0297-0_28

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