A note on eigenvalues of signed graphs

被引：3
|
作者：
Sun, Gaoxing [1 ]
Liu, Feng [2 ]
Lan, Kaiyang [2 ]
机构：
[1] Henan Normal Univ, Coll Math & Informat Sci, Xinxiang 453007, Peoples R China
[2] Fuzhou Univ, Ctr Discrete Math, Fuzhou 350003, Fujian, Peoples R China
来源：
LINEAR ALGEBRA AND ITS APPLICATIONS | 2022年 / 652卷
关键词：
Signed graph; Eigenvalue; Balanced clique number; SPECTRAL-RADIUS; BOUNDS; NUMBERS; CLIQUE;
D O I：
10.1016/j.laa.2022.07.010
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
Suppose that sigma is a signed graph with n vertices and m edges. Let lambda 1 > lambda 2 > . . . > lambda n be the eigenvalues of sigma. A signed graph is called balanced if each of its cycles contains an even number of negative edges, and unbalanced otherwise. Let wb be the balanced clique number of sigma, which is the maximum order of a balanced complete subgraph of sigma. In this paper, we prove that lambda 1 <= root 2 omega b - 1/omega bm. This inequality extends a conjecture of ordinary graphs, which was confirmed by Nikiforov (2002) [8], to the signed case. In addition, we completely characterize the signed graphs with -1 < lambda 2 < 0.(c) 2022 Elsevier Inc. All rights reserved.
引用
收藏
页码：125 / 131
页数：7
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