On the symmetry of the Laplacian spectra of signed graphs
Fatihcan M. Atay and Bobo Hua
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Submission date: 17. Nov. 2014 (revised version: November 2014)
published in: Linear algebra and its applications, 495 (2016), p. 24-37
DOI number (of the published article): 10.1016/j.laa.2016.01.027
MSC-Numbers: 05C50, 05C22, 39A12
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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.