On the Seidel spectrum of threshold graphs

In this paper, we analyse spectral properties of Seidel matrix (denoted by $S$) of connected threshold graphs. We compute the characteristic polynomial and determinant of Seidel matrix of threshold graphs. We derive formulas for the multiplicity of the eigenvalues $\pm 1$ of $S$. Further we determine threshold graphs with at most 5 distinct Seidel eigenvalues. Finally we construct families of Seidel cospectral threshold graphs.

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