首页|Toughness and normalized Laplacian eigenvalues of graphs
Toughness and normalized Laplacian eigenvalues of graphs
扫码查看
点击上方二维码区域，可以放大扫码查看
原文链接
NSTL
Elsevier
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.
NSTL
Elsevier
