论文标题
霍夫曼定理：新发现的重新访问
A Hoffman's Theorem: a revisit with new discovery
论文作者
论文摘要
1972年，A。J。Hoffman证明了他的著名定理，这些定理是关于非阴性对称积分矩阵的光谱半径的限制点，小于$ \ sqrt {2+ \ sqrt {5}} $。在本文中，在给出了霍夫曼定理的新版本之后，我们获得了两个普遍的版本，适用于具有分数元素的非阴性对称矩阵。作为推论，我们获得了另一个替代版本，内容涉及（无标志性的）图形矩阵的光谱半径小于$ 2+ {\ tiny \ frac {{\;} 1 {\;}}}} {3} {3} {3} 6 \ sqrt {33}）^{\ frac {{{\;} 1 {\;}}} {3}}}} +（54 + 6 \ sqrt {33}）^{\ frac {\ frac {{\;} {\;} 1 {\;}}}}}}}我们还讨论了如何采用我们的方法来研究等缘线。
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 $2+ {\tiny \frac{{\;}1{\;}}{3}\left((54 - 6\sqrt{33})^{\frac{{\;}1{\;}}{3}} + (54 + 6\sqrt{33})^{\frac{{\;} 1{\;}}{3}} \right)}$. We also discuss how our approach could be fruitfully employed to investigate equiangular lines.
