ABSTRACT

In this article, we present the restricted numerical for the Laplacian matrix of a directed graph (digraph). We motivate our interest in the restricted numerical range by its close connection to the algebraic connectivity of a digraph. Moreover, we show that the restricted numerical range can be used to characterize digraphs, some of which are not determined by their Laplacian spectrum. Finally, we identify a new class of digraphs that are characterized by having a real restricted numerical range.

中文翻译：

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关于有向图的拉普拉斯矩阵的有限数值范围

抽象的

在本文中，我们介绍了有向图（有向图）的拉普拉斯矩阵的受限数值。我们通过限制数字范围与有向图的代数连通性紧密联系，激发了我们对有限数字范围的兴趣。此外，我们证明了有限的数值范围可用于表征有向图，其中一些不是由其拉普拉斯谱确定的。最后，我们确定一类新的有向图，其特征是具有一个有限的数值范围。