Please use this identifier to cite or link to this item: http://hdl.handle.net/2080/3616
Title: On the seidel matrix of threshold graphs
Authors: Mandal, Santanu
Mehatari, Ranjit
Keywords: threshold graph
Seidel matrix
quotient matrix
Seidel energy
Issue Date: 2021
Citation: International Conference on Linear Algebra and its Applications (ICLAA 2021), Manipal Academy of Higher Education, Manipal, 15 - 17 December 2021
Abstract: Threshold graph has an important role in graph theory and several applied arreas such as computer science, scheduling theory etc. Here threshold graphs with its binary string representation are considered. Let G be a connected threshold graph with adjacency and Seidel matrix A and S respectively. Then S = J − I − 2A. We study the spectral properties of S. A recurrence formula for characteristic polynomial of S, multiplicity of the eigenvalues ±1 of S and eigenvalue bounds are obtained. Characterisation of threshold graphs with at most five distinct Seidel eigenvalue is shown also. We obtain several bounds on Seidel energy of G. It is shown that our bound is better than Haemers’ bound in practical. Finally, we prove a very uncommon result for threshold graphs: two threshold graphs may be cospectral on Seidel matrix. Here we define a class of such threshold graphs
Description: Copyright of this paper is with proceedings publisher
URI: http://hdl.handle.net/2080/3616
Appears in Collections:Conference Papers

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