文献类型：期刊文献

英文题名：The nullity of a graph with fractional matching number

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：345

期号：8

外文期刊名：DISCRETE MATHEMATICS

收录：;WOS:【SCI-EXPANDED(收录号:WOS:000821782600017)】；

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

语种：英文

外文关键词：Graph; Eigenvalue; Nullity; Fractional matching number

摘要：Let Gbe a simple graph with n(G) vertices and e(G) edges. Denoted by eta(G) and m* (G) the nullity and the fractional matching number of G, respectively. The dimension of cycle space of Gis defined as c(G) = e(G) - n(G) + omega(G), where omega(G) denotes the number of connected components of G. In this paper, we prove that n(G) - 2m* (G) <= eta(G) <= n(G) - 2m* (G) + 2c(G) for a graph G, which improves the main results of Wang and Wong (2014) [19] and Ma and Fang (2019) [11], respectively. Furthermore, all graphs with nullity eta(G) = n - 2m* (G) + 2c(G) are determined. We also prove that there is no graph with nullity eta(G) = n - 2m* (G) + 2c(G) - 1; and for fixed c(G), infinitely many connected graphs with nullity n - 2m* (G) + 2c(G) - k(0 <= k <= 2c(G), k not equal 1) are also constructed. As an application of the above results, we also prove that if Gis nonsingular, then Ghas a fractional perfect matching. (c) 2022 Elsevier B.V. All rights reserved.