On the Seidel spectrum of threshold graphs

Publications

On the Seidel spectrum of threshold graphs

Year : 2024

Publisher : Indian National Science Academy

Source Title : Indian Journal of Pure and Applied Mathematics

Document Type :

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 ±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.