On the Inertia Index of a Mixed Graph in Terms of the Matching Number

作     者：Sheng-jie HE Rong-Xia HAO Ai-mei YU Sheng-jie HE;Rong-Xia HAO;Ai-mei YU

作者机构：School of Mathematics and StatisticsBeijing Jiaotong UniversityBeijing 100044China 

出 版 物：《Acta Mathematicae Applicatae Sinica》 (应用数学学报（英文版）)

年 卷 期：2023年第39卷第3期

页      面：591-604页

核心收录：

学科分类：07[理学] 070104[理学-应用数学] 0701[理学-数学] 

基　　金：the National Natural Science Foundation of China (Nos. 11971054 and 12161141005) the Fundamental Research Funds for the Central Universities (No. 2016JBM071)。 

主　　题：Inertia index Mixed graph Matching number 

摘      要：A mixed graph G^(-) is obtained by orienting some edges of G, where G is the underlying graph of G^(-) . The positive inertia index, denoted by p~+( G), and the negative inertia index, denoted by n~-(G^(-) ), of a mixed graph G^(-) are the integers specifying the numbers of positive and negative eigenvalues of the Hermitian adjacent matrix of G^(-) , respectively. In this paper, the positive and negative inertia indices of the mixed unicyclic graphs are studied. Moreover, the upper and lower bounds of the positive and negative inertia indices of the mixed graphs are investigated, and the mixed graphs which attain the upper and lower bounds are characterized respectively.