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

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

2007-05-24

arxiv.org/abs/0705.3599v1

Mathematics

Combinatorics

33 pages, 18 figures

Scientific paper

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).

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