On the Seidel spectrum of threshold graphs

Santanu Mandal () and Ranjit Mehatari ()
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Santanu Mandal: National Institute of Technology Rourkela
Ranjit Mehatari: National Institute of Technology Rourkela

Indian Journal of Pure and Applied Mathematics, 2024, vol. 55, issue 4, 1290-1301

Abstract: Abstract We consider a connected threshold graph G with A, S as its adjacency matrix and Seidel matrix respectively. In this paper several spectral properties of S are analysed. We compute the characteristic polynomial and determinant of S. A formula for the multiplicity of the Seidel eigenvalues $$\pm 1$$ ± 1 and characterisation of threshold graphs with at most five distinct Seidel eigenvalues are derived. Finally it is shown that two non isomorphic threshold graphs may be cospectral for S.

Keywords: Threshold graph; Seidel matrix; Quotient matrix; Seidel cospectral; 05C50 (search for similar items in EconPapers)
Date: 2024
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DOI: 10.1007/s13226-023-00436-9

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