Bounds for the rank of a complex unit gain graph in terms of its maximum degree

被引：8

作者：

Lu, Yong ^{[1
]}

Wu, Jingwen ^{[1
]}

机构：

[1] Jiangsu Normal Univ, Sch Math & Stat, Xuzhou 221116, Jiangsu, Peoples R China

来源：

LINEAR ALGEBRA AND ITS APPLICATIONS | 2021年 / 610卷

基金：

中国国家自然科学基金;

关键词：

Complex unit gain graphs; Rank of graphs; Maximum degree;

D O I：

10.1016/j.laa.2020.09.035

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

Let Phi = (G, phi) be a T-gain graph with maximum degree Delta. Zhou et al. (2018) [3.5] gave a lower bound of the rank of simple graphs in items of maximum degree. Motivated by above result, in this paper, we extend this result to T-gain graphs. We obtain that r(Phi) >= n/Delta for a T-gain graph. All the corresponding extremal graphs are characterized. Furthermore, we also obtain some other results about the rank of T-gain graphs. (C) 2020 Elsevier Inc. All rights reserved.

引用

页码：73 / 85

页数：13

共 44 条

[1] The rank of a complex unit gain graph in terms of the rank of its underlying graph
Lu, Yong
Wang, Ligong
Zhou, Qiannan
JOURNAL OF COMBINATORIAL OPTIMIZATION, 2019, 38 (02) : 570 - 588
[2] The rank of a complex unit gain graph in terms of the rank of its underlying graph
Yong Lu
Ligong Wang
Qiannan Zhou
Journal of Combinatorial Optimization, 2019, 38 : 570 - 588
[3] Bounds for the rank of a complex unit gain graph in terms of the independence number
He, Shengjie
Hao, Rong-Xia
Yu, Aimei
LINEAR & MULTILINEAR ALGEBRA, 2022, 70 (07): : 1382 - 1402
[4] On bounds of Aα-eigenvalue multiplicity and the rank of a complex unit gain graph
Samanta, Aniruddha
DISCRETE MATHEMATICS, 2023, 346 (09)
[5] The rank of a complex unit gain graph in terms of the matching number
He, Shengjie
Hao, Rong-Xia
Dong, Fengming
LINEAR ALGEBRA AND ITS APPLICATIONS, 2020, 589 : 158 - 185
[6] The gap between the rank of a complex unit gain graph and its underlying graph
Du, Kexin
Lu, Yong
Zhou, Qiannan
DISCRETE APPLIED MATHEMATICS, 2024, 357 : 399 - 412
[7] Bounds for the energy of a complex unit gain graph
Samanta, Aniruddha
Kannan, M. Rajesh
LINEAR ALGEBRA AND ITS APPLICATIONS, 2021, 612 : 1 - 29
[8] NEW UPPER BOUNDS FOR THE BONDAGE NUMBER OF A GRAPH IN TERMS OF ITS MAXIMUM DEGREE AND EULER CHARACTERISTIC
Huang, Jia
Shen, Jian
ARS COMBINATORIA, 2018, 140 : 373 - 387
[9] A lower bound of the rank of a signed graph in terms of order and maximum degree
Lu, Yong
Xu, Wei-Ru
SCIENCEASIA, 2021, 47 (06): : 779 - 784
[10] Bounds on the independence number of a graph in terms of order, size and maximum degree
Rad, Nader Jafari
Sharifi, Elahe
DISCRETE APPLIED MATHEMATICS, 2017, 217 : 210 - 219

← 1 2 3 4 5 →