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- W3115429072 abstract "In 1972, A. J. Hoffman proved his celebrated theorem concerning the limit points of spectral radii of non-negative symmetric integral matrices less than $sqrt{2+sqrt{5}}$. In this paper, after giving a new version of Hoffman's theorem, we get two generalized versions of it applicable to non-negative symmetric matrices with fractional elements. As a corollary, we obtain another alternative version about the limit points of spectral radii of (signless) Laplacian matrices of graphs less than $2+ {tiny frac{{;}1{;}}{3}left((54 - 6sqrt{33})^{frac{{;}1{;}}{3}} + (54 + 6sqrt{33})^{frac{{;} 1{;}}{3}} right)}$. We also discuss how our approach could be fruitfully employed to investigate equiangular lines." @default.
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- W3115429072 date "2020-12-27" @default.
- W3115429072 modified "2023-09-25" @default.
- W3115429072 title "A Hoffman's Theorem: a revisit with new discovery" @default.
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- W3115429072 doi "https://doi.org/10.48550/arxiv.2012.14090" @default.
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