On the symmetry of the Laplacian spectra of signed graphs

2014/11/22 by Fatihcan M. Atay, Bobo Hua
Computer Science · Mathematics · #Combinatorics #Geometry #Graph #Graph theory and applications #Laplace operator #Laplacian matrix #Mathematical analysis #Mathematics #Matrix Theory and Algorithms #Physics #Pure mathematics #Quantum graph #Quantum mechanics #Spectral Theory in Mathematical Physics #Spectral line #Spectrum (functional analysis) #Symmetry (geometry) #math.CO #math.SP #msc:05C22 #msc:05C50 #msc:39A12

paper · pdf · doi:10.1016/j.laa.2016.01.027

published as Linear Algebra and its Applications, Vol. 495, pp. 24-37 (2016)

arxiv created 2014/11/22 · openalex publication_date 2016/01/22 · arxiv updated 2016/02/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

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.

Citations

• Spectral graph theory [CBMS Conference on Recent Advances in Spectral Graph Theory held at California State University at Fresno, June 6 - 10. 1994]