Abstract
In this article, we investigate the relationship between algebraic and vertex connectivities of graphs, studying the difference between these two parameters. Cographs belong to the class of Laplacian integral graphs. In this paper, we prove that the algebraic and vertex connectivities of these graphs are equal. We also build infinite families of Laplacian and non-Laplacian integral graphs satisfying distinct relationships between these connectivities.
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Acknowledgements
R. Del-Vecchio was partially supported by Conselho Nacional de Desenvolvimento Científico e Tecnológico, CNPq-Grant 306262/2019-3 and M.A.A. de Freitas was partially supported by CNPq-Grant 313335/2020-6.
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Communicated by Aida Abiad.
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Lucas, C.L.d.A.V.M., Del-Vecchio, R.R., de Freitas, M.A.A. et al. Relationships between algebraic connectivity and vertex connectivity. Comp. Appl. Math. 41, 105 (2022). https://doi.org/10.1007/s40314-022-01786-6
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DOI: https://doi.org/10.1007/s40314-022-01786-6