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arXiv · 1411.6113

On the symmetry of the Laplacian spectra of signed graphs

Fatihcan M. Atay·Bobo Hua
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Abstract

We study the symmetry properties of the spectra of normalized Laplacians on signed graphs. We find a new machinery that generates symmetric spectra for signed graphs, which includes bipartiteness of unsigned graphs as a special case. Moreover, we prove a fundamental connection between the symmetry of the spectrum and the existence of damped two-periodic solutions for the discrete-time heat equation on the graph.

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Fatihcan M. Atay, Bobo Hua. 2014-11-22. On the symmetry of the Laplacian spectra of signed graphs. https://doi.org/10.1016/j.laa.2016.01.027

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