Bounds on the nullity, the H-rank and the Hermitian energy of a mixed graph

被引：7

作者：

Wei, Wei ^{[1
]}

Li, Shuchao ^{[1
]}

Ma, Hongping ^{[2
]}

机构：

[1] Cent China Normal Univ, Fac Math & Stat, Wuhan 430079, Hubei, Peoples R China

[2] Jiangsu Normal Univ, Sch Math & Stat, Xuzhou, Jiangsu, Peoples R China

来源：

LINEAR & MULTILINEAR ALGEBRA | 2021年 / 69卷 / 13期

基金：

中国国家自然科学基金;

关键词：

Mixed graphs; nullity; Hermitian energy; switching equivalence; ORIENTED GRAPH; SKEW-RANK; INDEPENDENCE NUMBER; MATCHING NUMBER; ADJACENCY MATRIX; TERMS; ORDER;

D O I：

10.1080/03081087.2019.1679702

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Given an n-vertex graph G with maximum degree ?, the mixed graph is constructed from G by orienting some of its edges, where G is called the underlying graph of . Let be the H-rank of and let be the independence number of G. In this paper, we firstly determine the maximum nullity of n-vertex mixed graphs with maximum degree ?. The corresponding extremal graphs are identified. We secondly establish upper and lower bounds on , respectively. Finally, we characterize the relationship between the Hermitian energy and the H-rank of a?mixed graph.

引用

页码：2469 / 2490

页数：22

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