Toughness and normalized Laplacian eigenvalues of graphs

Xueyi Huang, Kinkar Chandra Das and Shunlai Zhu

Applied Mathematics and Computation, 2022, vol. 425, issue C

Abstract: Given a connected graph G, the toughness τG is defined as the minimum value of the ratio |S|/ωG−S, where S ranges over all vertex cut sets of G, and ωG−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 τG 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).

Keywords: Toughness; Normalized Laplacian eigenvalue; Algebraic connectivity (search for similar items in EconPapers)
Date: 2022
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Citations: View citations in EconPapers (1)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:425:y:2022:i:c:s009630032200159x

DOI: 10.1016/j.amc.2022.127075

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