Eigenvalues and chromatic number of a signed graph

被引：8
|
作者：
Wang, Wei [1 ]
Yan, Zhidan [1 ]
Qian, Jianguo [2 ]
机构：
[1] Anhui Polytech Univ, Sch Math Phys & Finance, Wuhu 241000, Peoples R China
[2] Xiamen Univ, Sch Math Sci, Xiamen 361005, Peoples R China
来源：
LINEAR ALGEBRA AND ITS APPLICATIONS | 2021年 / 619卷
基金：
中国国家自然科学基金;
关键词：
Signed graph; Eigenvalue; Chromatic number; Clique; SPECTRAL BOUNDS; CLIQUE;
D O I：
10.1016/j.laa.2021.02.018
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
For a signed graph Sigma, let chi(Sigma), lambda(1) and lambda(n) be the chromatic number, the maximum eigenvalue and the minimum eigenvalue of Sigma, respectively. This paper proves that, for any nonempty signed graph Sigma with n vertices, chi(Sigma) >= max {1 + lambda(1)/vertical bar lambda(n)vertical bar, n/n - lambda(1)}. These two bounds extend the classical spectral lower bounds of Hoffman and Cvetkovic for an ordinary graph, respectively. (C) 2021 Elsevier Inc. All rights reserved.
引用
收藏
页码：137 / 145
页数：9
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