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MiS Preprint

On the symmetry of the Laplacian spectra of signed graphs

Fatihcan M. Atay and Bobo Hua


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.

MSC Codes:
05C50, 05C22, 39A12

Related publications

2016 Repository Open Access
Bobo Hua and Fatihcan M. Atay

On the symmetry of the Laplacian spectra of signed graphs

In: Linear algebra and its applications, 495 (2016), pp. 24-37