| 混合图的Hermitian邻接矩阵的零维数 |
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| 引用本文： | 田凤雷,王登银. 混合图的Hermitian邻接矩阵的零维数[J]. 数学研究及应用, 2018, 38(1): 23-33 |
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| 作者姓名： | 田凤雷 王登银 |
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| 作者单位： | 中国矿业大学数学学院, 江苏 徐州 221116,中国矿业大学数学学院, 江苏 徐州 221116 |
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| 基金项目： | 国家自然科学基金(Grant No.11571360). |
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| 摘 要： | A mixed graph means a graph containing both oriented edges and undirected edges. The nullity of the Hermitian-adjacency matrix of a mixed graph G, denoted by ηH(G),is referred to as the multiplicity of the eigenvalue zero. In this paper, for a mixed unicyclic graph G with given order and matching number, we give a formula on ηH(G), which combines the cases of undirected and oriented unicyclic graphs and also corrects an error in Theorem 4.2 of [Xueliang LI, Guihai YU. The skew-rank of oriented graphs. Sci. Sin. Math., 2015, 45:93-104(in Chinese)]. In addition, we characterize all the n-vertex mixed graphs with nullity n-3, which are determined by the spectrum of their Hermitian-adjacency matrices.
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| 关 键 词： | 零维数 混合图 单圈图 Hermitian 邻接矩阵 |
| 收稿时间： | 2016-11-30 |
| 修稿时间： | 2017-09-01 |
Nullity of Hermitian-Adjacency Matrices of Mixed Graphs |
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| Fenglei TIAN and Dein WONG. Nullity of Hermitian-Adjacency Matrices of Mixed Graphs[J]. Journal of Mathematical Research with Applications, 2018, 38(1): 23-33 |
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| Authors: | Fenglei TIAN and Dein WONG |
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| Affiliation: | School of Mathematics, China University of Mining and Technology, Jiangsu 221116, P. R. China and School of Mathematics, China University of Mining and Technology, Jiangsu 221116, P. R. China |
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| Abstract: | A mixed graph means a graph containing both oriented edges and undirected edges. The nullity of the Hermitian-adjacency matrix of a mixed graph $G$, denoted by $eta_H(G)$, is referred to as the multiplicity of the eigenvalue zero. In this paper, for a mixed unicyclic graph $G$ with given order and matching number, we give a formula on $eta_H(G)$, which combines the cases of undirected and oriented unicyclic graphs and also corrects an error in Theorem 4.2 of [Xueliang LI, Guihai YU. The skew-rank of oriented graphs. Sci. Sin. Math., 2015, 45: 93-104 (in Chinese)]. In addition, we characterize all the $n$-vertex mixed graphs with nullity $n-3$, which are determined by the spectrum of their Hermitian-adjacency matrices. |
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| Keywords: | nullity mixed graph unicyclic graph Hermitian-adjacency matrix |
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