论文标题
最小特征值大于$ - \ frac {\ sqrt {5} +1} {2} $的混合图
Mixed graphs with smallest eigenvalue greater than $-\frac{\sqrt{5}+1}{2}$
论文作者
论文摘要
用有限特征值表征图表的经典问题可能可以追溯到史密斯（Smith）在1970年的作品。特别是，对特征值最小的图表的研究不少于$ -2 $，引起了广泛的关注。混合图是无向图的自然概括。在本文中，我们完全表征了最小的Hermitian特征值大于$ - \ frac {\ sqrt {5} +1} {2} $的混合图，该图由三个无限的混合图和$ 30 $零散的混合图组成。顺便说一句，我们得到了一类新的混合图形切换，等效于它们的基础图。
The classical problem of characterizing the graphs with bounded eigenvalues may date back to the work of Smith in 1970. Especially, the research on graphs with smallest eigenvalues not less than $-2$ has attracted widespread attention. Mixed graphs are natural generalization of undirected graphs. In this paper, we completely characterize the mixed graphs with smallest Hermitian eigenvalue greater than $-\frac{\sqrt{5}+1}{2}$, which consists of three infinite classes of mixed graphs and $30$ scattered mixed graphs. By the way, we get a new class of mixed graphs switching equivalent to their underlying graphs.
