A Frucht Theorem for Quantum Graphs

DOI10.1007/978-3-0348-0297-0_28zbMATH Open1254.05076arXiv1003.2529OpenAlexW1793773483MaRDI QIDQ3143996

Delio Mugnolo

Publication date: 6 December 2012

Published in: Spectral Theory, Mathematical System Theory, Evolution Equations, Differential and Difference Equations (Search for Journal in Brave)

Abstract: A celebrated theorem due to R. Frucht states that, roughly speaking, each group is 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 Schr"odinger equations on a metric graph, after suitably defining the notion of symmetry.

Full work available at URL: https://arxiv.org/abs/1003.2529

zbMATH Keywords

quantum graphsalgebraic graph theorysymmetries for evolution equations

Mathematics Subject Classification ID

Graphs and abstract algebra (groups, rings, fields, etc.) (05C25) Symmetric groups (20B30) Symmetries, invariants, etc. in context of PDEs (35B06) Quantum mechanics on special spaces: manifolds, fractals, graphs, lattices (81Q35)

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