文献类型：期刊文献

英文题名：A sharp upper bound of the nullity of a connected graph in terms of order and maximum degree

作者：Wang, Zhi-Wen[1];Guo, Ji-Ming[1]

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

年份：2020

卷号：584

起止页码：287

外文期刊名：LINEAR ALGEBRA AND ITS APPLICATIONS

收录：;EI(收录号：20193907473141);WOS:【SCI-EXPANDED(收录号:WOS:000495478900015)】；

基金：This research is supported by NSFC (No. 11371372).

语种：英文

外文关键词：Rank; Nullity; Graph

摘要：The nullity eta(G) of G is the multiplicity of 0 as an eigenvalue of A(G). In this paper, we completely solve the following conjecture proposed by Zhou, Wong and Sun in [Linear Algebra and its Applications, 555 (2018) 314-320]: Let G be a connected graph of order n with nullity eta(G) and the maximum degree Delta >= 2. Then eta(G) <= (Delta - 2)n + 2/Delta - 1, the equality holds if and only if G congruent to C-n (n equivalent to 0 (mod 4)) or G congruent to K-Delta,K-Delta. (C) 2019 Elsevier Inc. All rights reserved.