Isospectral graphs with identical nodal counts

Details Isospectral graphs with identical nodal counts Isospectral graphs with identical nodal counts

2011-10-02

arxiv.org/abs/1110.0158v1

Physics

Mathematical Physics

Scientific paper

According to a recent conjecture, isospectral objects have different nodal
count sequences. We study generalized Laplacians on discrete graphs, and use
them to construct the ?rst non-trivial counter-examples to this conjecture. In
addition, these examples demonstrate a surprising connection between
isospectral discrete and quantum graphs.

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