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\(\ell \)-Connectivity, Integrity, Tenacity, Toughness and Eigenvalues of Graphs

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Abstract

Using the eigenvalues of a graph to reflect its structural properties is a central topic in spectral graph theory. Especially, the relationships between the eigenvalues of a graph and its structural parameters have been studied extensively. In this paper, we explore the relationships between the (normalized) Laplacian eigenvalues of a graph and its \(\ell \)-connectivity, integrity, tenacity and toughness. Some of our results extend or improve the related existing results.

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Acknowledgements

The authors would like to thank the anonymous referees for their constructive corrections and valuable comments on this paper, which have considerably improved the presentation of this paper.

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Authors and Affiliations

  1. School of Mathematics and Statistics, Minnan Normal University, Zhangzhou, 363000, People’s Republic of China

    Hongzhang Chen & Jianxi Li

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  1. Hongzhang Chen
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  2. Jianxi Li
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Correspondence to Jianxi Li.

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Communicated by Ismael G. Yero.

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Partially supported by NSF of China (No. 12171089); NSF of Fujian (No. 2021J02048)

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Chen, H., Li, J. \(\ell \)-Connectivity, Integrity, Tenacity, Toughness and Eigenvalues of Graphs. Bull. Malays. Math. Sci. Soc. 45, 3307–3320 (2022). https://doi.org/10.1007/s40840-022-01381-2

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  • DOI: https://doi.org/10.1007/s40840-022-01381-2

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