Abstract: The Hermitian adjacency matrix of a mixed graph is a conjugate matrix and its all eigenvalues are called H-spectrum of the mixed graph. It has many of the properties that are most useful for dealing with mixed graphs. In this paper, H-Estrada index of the mixed graph is introduced which is a new H-spectrum-based invariant of the mixed graph. Its mathematical properties are studied by mathematical analysis.

Key words: mixed graph, Hermitian adjacency matrix, H-Estrada index

摘要： 混合图的Hermitian邻接矩阵是共轭矩阵，其全体特征值称为混合图的H-谱。借助该矩阵的许多性质能更有效地研究混合图。基于H-谱引出混合图的一个重要拓扑指标——H-Estrada指标。拟用数学分析的方法，对其性质做数理研究。

关键词: 混合图, Hermitian邻接矩阵, H-Estrada指标