2020/12/28 by Jianfeng Wang, Jing Wang, Wang, Jianfeng +3
Computer Science · Mathematics · #05C50 #Advanced Topics in Algebra #Combinatorics (math.CO) #FOS: Mathematics #Graph theory and applications #Matrix Theory and Algorithms
paper · pdf · doi:10.48550/arxiv.2012.14090
openalex publication_date 2020/12/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In 1972, A. J. Hoffman proved his celebrated theorem concerning the limit points of spectral radii of non-negative symmetric integral matrices less than √(2+√(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((54 - 6√(33))^\frac 1 3 + (54 + 6√(33))^\frac 1 3 ). We also discuss how our approach could be fruitfully employed to investigate equiangular lines.