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Which Graphs have Non-integral Spectra?

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The eigenvalues of a graph are algebraic integers in some algebraic extension of the rationals. We investigate the algebraic degree of these eigenvalues with respect to graph-theoretical properties. We obtain quantitative results showing that a graph with large diameter must have some eigenvalues of large algebraic degree.

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The authors are grateful to the anonymous referee for her or his valuable corrections and comments to improve the readability of the article and for introducing us to the Biggs-Smith graph and the doubled Odd graphs.

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Correspondence to Jörn Steuding.

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Mönius, K., Steuding, J. & Stumpf, P. Which Graphs have Non-integral Spectra?. Graphs and Combinatorics 34, 1507–1518 (2018).

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