Spectral symmetry in conference matrices
Haemers,Willem H. Parsaei Majd,Leila
Haemers,Willem H.
Parsaei Majd,Leila
Abstract
A conference matrix of order n is an n× n matrix C with diagonal entries 0 and off-diagonal entries ± 1 satisfying CC⊤= (n- 1) I. If C is symmetric, then C has a symmetric spectrum Σ (that is, Σ = - Σ) and eigenvalues ±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.
Description
Funding Information: The research of the second author was funded by Iranian National Science Foundation (INSF) under the contract No. 98021291. Publisher Copyright: © 2021, The Author(s). Copyright: Copyright 2021 Elsevier B.V., All rights reserved.
Date
2022-09
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Volume Title
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Research Projects
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Keywords
Conference matrix, Paley graph, Seidel matrix, Signed graph, Symmetric spectrum
Citation
Haemers, W H & Parsaei Majd, L 2022, 'Spectral symmetry in conference matrices', Designs Codes and Cryptography, vol. 90, pp. 1983-1990. https://doi.org/10.1007/s10623-021-00858-8
License
info:eu-repo/semantics/openAccess