文献类型：期刊文献

英文题名：Toughness and normalized Laplacian eigenvalues of graphs

作者：Huang, Xueyi[1,2];Das, Kinkar Chandra[2];Zhu, Shunlai[1]

机构：[1]East China Univ Sci & Technol, Sch Math, Shanghai 200237, Peoples R China;[2]Sungkyunkwan Univ, Dept Math, Suwon 16419, South Korea

年份：2022

卷号：425

外文期刊名：APPLIED MATHEMATICS AND COMPUTATION

收录：;EI(收录号：20221211817167);WOS:【SCI-EXPANDED(收录号:WOS:000793131700013)】；

基金：The authors are much grateful to two anonymous referees for their valuable comments on our paper, which have consid-erably improved the presentation of this paper. X. Huang is supported by the National Natural Science Foundation of China (Grant No. 11901540) . K. C. Das is supported by National Research Foundation funded by the Korean government (Grant No. 2021R1F1A1050646) . S. Zhu is supported by the Undergraduate Training Program on Innovation and Entrepreneurship (Grant No. X202110251335) .

语种：英文

外文关键词：Toughness; Normalized Laplacian eigenvalue; Algebraic connectivity

摘要：Given a connected graph G , the toughness tau G is defined as the minimum value of the ratio |S|/omega(G-S), where S ranges over all vertex cut sets of G , and omega(G-S) is the number of connected components in the subgraph G - S obtained by deleting all vertices of S from G . In this paper, we provide a lower bound for the toughness tau(G) in terms of the maximum degree, minimum degree and normalized Laplacian eigenvalues of G . This can be viewed as a slight generalization of Brouwer's toughness conjecture, which was confirmed by Gu (2021). Furthermore, we give a characterization of those graphs attaining the two lower bounds regarding toughness and Laplacian eigenvalues provided by Gu and Haemers (2022). (c) 2022 Elsevier Inc. All rights reserved.