文献类型：期刊文献

英文题名：Bounds of nullity for complex unit gain graphs

作者：Chen, Qian-Qian[1,2];Guo, Ji-Ming[2]

机构：[1]Yancheng Teachers Univ, Sch Math & Stat, Yancheng 224002, Jiangsu, Peoples R China;[2]East China Univ Sci & Technol, Sch Math, Shanghai 200237, Peoples R China

年份：2024

卷号：699

起止页码：569

外文期刊名：LINEAR ALGEBRA AND ITS APPLICATIONS

收录：;EI(收录号：20243116778617);WOS:【SCI-EXPANDED(收录号:WOS:001282597200001)】；

基金：This work is supported by NSFC (No. 12171154) .

语种：英文

外文关键词：Complex unit gain graph; Eigenvalue; Nullity; Block

摘要：A complex unit gain graph, or T-gain graph, is a triple Phi = ( C, T , p ) comprised of a simple graph C as the underlying graph of Phi, the set of unit complex numbers T = { z is an element of C : | z | = 1}, }, and a gain function p : (E) over right arrow -> T with the property that p ( e ij ) = p ( e ji ) -1 . A cactus graph is a connected graph in which any two cycles have at most one vertex in common. In this paper, we firstly show that there does not exist a complex unit gain graph with nullity n ( C ) -2 m ( C ) +2c(C) c ( C ) -1, where n ( C ), m ( C ) and c ( C ) are the order, matching number, and cyclomatic number of C . Next, we provide a lower bound on the nullity for connected complex unit gain graphs and an upper bound on the nullity for complex unit gain bipartite graphs. Finally, we characterize all non-singular complex unit gain bipartite cactus graphs, which generalizes a result in Wong et al. (2022) [30]. (c) 2024 Elsevier Inc. All rights are reserved, including those for text and data mining, AI training, and similar technologies.