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Mathematics > Combinatorics

arXiv:1907.04349 (math)
[Submitted on 9 Jul 2019]

Title:Open problems in the spectral theory of signed graphs

Authors:Francesco Belardo, Sebastian M. Cioabă, Jack H. Koolen, Jianfeng Wang
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Abstract:Signed graphs are graphs whose edges get a sign $+1$ or $-1$ (the signature). Signed graphs can be studied by means of graph matrices extended to signed graphs in a natural way. Recently, the spectra of signed graphs have attracted much attention from graph spectra specialists. One motivation is that the spectral theory of signed graphs elegantly generalizes the spectral theories of unsigned graphs. On the other hand, unsigned graphs do not disappear completely, since their role can be taken by the special case of balanced signed graphs.
Therefore, spectral problems defined and studied for unsigned graphs can be considered in terms of signed graphs, and sometimes such generalization shows nice properties which cannot be appreciated in terms of (unsigned) graphs. Here, we survey some general results on the adjacency spectra of signed graphs, and we consider some spectral problems which are inspired from the spectral theory of (unsigned) graphs.
Comments: 22 pages, 4 figures, submitted to The Art of Discrete and Applied Mathematics, this https URL
Subjects: Combinatorics (math.CO); Discrete Mathematics (cs.DM)
MSC classes: 05C22, 05C50
Cite as: arXiv:1907.04349 [math.CO]
  (or arXiv:1907.04349v1 [math.CO] for this version)
  https://doi.org/10.48550/arXiv.1907.04349

Submission history

From: Sebastian M. Cioabă [view email]
[v1] Tue, 9 Jul 2019 18:12:51 UTC (73 KB)
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