scholarly journals Connected non-complete signed graphs which have symmetric spectrum but are not sign-symmetric

2021 ◽  
Vol 1 ◽  
pp. 100007
Author(s):  
Zoran Stanić
Keyword(s):  
Signed Graphs ◽  
Symmetric Spectrum

scholarly journals Spectral symmetry in conference matrices

2021 ◽  
Author(s):  
Willem H. Haemers ◽  
Leila Parsaei Majd
Keyword(s):  
Signed Graphs ◽  
Adjacency Matrices ◽  
Seidel Matrices ◽  
Principal Submatrices ◽  
Symmetric Spectrum

AbstractA conference matrix of order n is an $$n\times n$$ n × n matrix C with diagonal entries 0 and off-diagonal entries $$\pm 1$$ ± 1 satisfying $$CC^\top =(n-1)I$$ C C ⊤ = ( n - 1 ) I . If C is symmetric, then C has a symmetric spectrum $$\Sigma $$ Σ (that is, $$\Sigma =-\Sigma $$ Σ = - Σ ) and eigenvalues $$\pm \sqrt{n-1}$$ ± n - 1 . We show that many principal submatrices of C also have symmetric spectrum, which leads to examples of Seidel matrices of graphs (or, equivalently, adjacency matrices of complete signed graphs) with a symmetric spectrum. In addition, we show that some Seidel matrices with symmetric spectrum can be characterized by this construction.

Note on Distance Coprime Signed Graphs

2018 ◽  
Vol 9 (10) ◽  
pp. 1473-1476
Author(s):  
K. V. Madhusudhan
Keyword(s):  
Signed Graphs

scholarly journals Resolution of indecomposable integral flows on signed graphs

2017 ◽  
Vol 340 (6) ◽  
pp. 1271-1286 ◽  
Author(s):  
Beifang Chen ◽  
Jue Wang ◽  
Thomas Zaslavsky
Keyword(s):  
Signed Graphs

Balancedness and spectra of signed graphs obtained by $$\dot{H}$$-join operation

2021 ◽  
Vol 40 (3) ◽  
Author(s):  
Peikang Zhang ◽  
Baofeng Wu ◽  
Changxiang He
Keyword(s):  
Signed Graphs

Signed graphs with stable maximum nullity at most two

2021 ◽  
Author(s):  
Marina Arav ◽  
F. Scott Dahlgren ◽  
Hein van der Holst
Keyword(s):  
Signed Graphs ◽  
Maximum Nullity
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