文献类型：期刊文献

英文题名：The rank of a signed graph

作者：Chen, Qian-Qian[1];Guo, Ji-Ming[1]

机构：[1]East China Univ Sci & Technol, Sch Math, Shanghai, Peoples R China

年份：2022

卷号：651

起止页码：407

外文期刊名：LINEAR ALGEBRA AND ITS APPLICATIONS

收录：;EI(收录号：20222912372519);WOS:【SCI-EXPANDED(收录号:WOS:000834142300002)】；

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

语种：英文

外文关键词：Signed graph; Matching number; Fractional matching number; Nonsingular

摘要：Let (G, sigma) be a signed graph with order n(G) and size e(G). The rank r(G, sigma) of (G, sigma) is the rank of A(G, sigma), where A(G, sigma) is the adjacency matrix of (G, sigma). Let m(G) be the matching number of G, m*(G) be the fractional matching number of G, and c(G) = e(G) - n(G) + 0(G) be the cyclomatic number of G with 0(G) the number of connected components. In this paper, we prove that 2m(G) - 2 kappa(G) <= r(G, sigma) <= 2m*(G) for any signed graph, kappa(G) is the number of even cycles in G. This improves the main result in He and Hao (2019) [10] saying that 2m(G) - 2c(G) <= r(G, sigma) <= 2m(G) + c(G). Moreover, we characterize all signed graphs with r(G, sigma) = 2m(G)-2 kappa(G) when kappa(G) = c(G) or c(G)-1. Furthermore, all nonsingular bipartite cycle-disjoint signed graphs are achieved in this paper. (C) 2022 Elsevier Inc. All rights reserved.