Integer symmetric matrices having all their eigenvalues in the interval [-2,2]

Abstract

We completely describe all integer symmetric matrices that have all their eigenvalues in the interval [-2,2]. Along the way we classify all signed graphs, and then all charged signed graphs, having all their eigenvalues in this same interval. We then classify subsets of the above for which the integer symmetric matrices, signed graphs and charged signed graphs have all their eigenvalues in the open interval (-2,2).

33 pages, 18 figures

Cited by in corpus (6)

• Survey article: Seventy years of Salem numbers
• Cyclotomic Matrices and Graphs over the ring of integers of some imaginary quadratic fields
• Quantum models as classical cellular automata
• Cyclotomic matrices over real quadratic integer rings
• Graph covers with two new eigenvalues
• Transitions between root subsets associated with Carter diagrams