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On sign-symmetric signed graphs. (English) Zbl 1465.05072

Summary: A signed graph is said to be sign-symmetric if it is switching isomorphic to its negation. Bipartite signed graphs are trivially sign-symmetric. We give new constructions of non-bipartite sign-symmetric signed graphs. Sign-symmetric signed graphs have a symmetric spectrum but not the other way around. We present constructions of signed graphs with symmetric spectra which are not sign-symmetric. This, in particular answers a problem posed by F. Belardo et al. [Art Discrete Appl. Math. 1, No. 2, Paper No. P2.10, 23 p. (2018; Zbl 1421.05052)].

MSC:

05C22 Signed and weighted graphs
05C50 Graphs and linear algebra (matrices, eigenvalues, etc.)

Citations:

Zbl 1421.05052
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References:

[1] S. Akbari, H. R. Maimani and L. Parsaei Majd, On the spectrum of some signed complete and complete bipartite graphs,Filomat32(2018), 5817-5826, doi:10.2298/fil1817817a. · Zbl 1499.05256
[2] F. Belardo, S. M. Cioab˘a, J. Koolen and J. Wang, Open problems in the spectral theory of signed graphs,Art Discrete Appl. Math.1(2018), #P2.10 (23 pages), doi:10.26493/2590-9770.1286. d7b. · Zbl 1421.05052
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