Nodal domains on isospectral quantum graphs: the resolution of isospectrality ?

Details Nodal domains on isospectral quantum graphs: the resolution of isospectrality ? Nodal domains on isospectral quantum graphs: the resolution of isospectrality ?

2006-08-14

arxiv.org/abs/nlin/0608031v3

Nonlinear Sciences

Chaotic Dynamics

Scientific paper

10.1088/0305-4470/39/45/009

We present and discuss isospectral quantum graphs which are not isometric. These graphs are the analogues of the isospectral domains in R2 which were introduced recently and are all based on Sunada's construction of isospectral domains. After presenting some of the properties of these graphs, we discuss a few examples which support the conjecture that by counting the nodal domains of the corresponding eigenfunctions one can resolve the isospectral ambiguity.

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