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.
Original language | English |
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Journal | Designs, Codes, and Cryptography |
DOIs | |
Publication status | E-pub ahead of print - Mar 2021 |
Keywords
- Conference matrix
- Paley graph
- Seidel matrix
- Signed graph
- Symmetric spectrum