Characterizing the mixed graphs with exactly one positive eigenvalue and its application to mixed graphs determined by their H-spectra
Characterizing the mixed graphs with exactly one positive eigenvalue and its application to mixed graphs determined by their H-spectra
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描述具有一个正特征值的混合图及其在由 H 谱确定的混合图上的应用
DOI：
10.1016/j.amc.2020.125279
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发表时间：
2020
影响因子：
4
通讯作者：
Jing Xu
中科院分区：
文献类型：
--
作者：
Bo-Jun Yuan;Yi Wang;Jing Xu
通过对简单图的一些边进行定向，得到一个混合图。混合图的正惯性指数定义为它的埃尔米特邻接矩阵的正特征值的个数，包括重数。本文研究了混合图的正惯性指数。我们的主要结果提供了一个具有正惯性指数1的混合图的特征。作为应用，我们给出了由H-谱确定的几类混合图。
A mixed graph is obtained by orienting some edges of a simple graph. The positive inertia index of a mixed graph is defined as the number of positive eigenvalues of its Hermitian adjacency matrix, including multiplicities. In this paper, we study the positive inertia indices of mixed graphs. Our main results provide a characterization of mixed graphs with positive inertia index 1. As an application, some classes of mixed graphs determined by theirH-spectra are fixed.