Spectral bounds for the connectivity of regular graphs with given order

Aida Abiad Monge*, Boris Brimkov, Xavier Martínez-Rivera, Suil O, Jingmei Zhang

*Corresponding author for this work

Research output: Contribution to journalArticleAcademicpeer-review

11 Citations (Web of Science)


The second-largest eigenvalue and second-smallest Laplacian eigenvalue of a graph are measures of its connectivity. These eigenvalues can be used to analyze the robustness, resilience, and synchronizability of networks, and are related to connectivity attributes such as the vertex- and edge-connectivity, isoperimetric number, and characteristic path length. In this paper, two upper bounds are presented for the second-largest eigenvalues of regular graphs and multigraphs of a given order which guarantee a desired vertex- or edge-connectivity. The given bounds are in terms of the order and degree of the graphs, and hold with equality for infinite families of graphs. These results answer a question of Mohar.
Original languageEnglish
Pages (from-to)428-443
JournalElectronic Journal of Linear Algebra
Publication statusPublished - 2018

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