Spectral bounds for the connectivity of regular graphs with given order

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

doi:10.13001/1081-3810.3675

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

QE Operations research

Research output: Contribution to journal › Article › Academic › peer-review

11 Citations (Web of Science)

Abstract

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 language	English
Pages (from-to)	428-443
Journal	Electronic Journal of Linear Algebra
Volume	34
DOIs	https://doi.org/10.13001/1081-3810.3675
Publication status	Published - 2018

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10.13001/1081-3810.3675

Cite this

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title = "Spectral bounds for the connectivity of regular graphs with given order",

abstract = "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.",

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AU - Abiad Monge, Aida

AU - Brimkov, Boris

AU - Martínez-Rivera, Xavier

AU - O, Suil

AU - Zhang, Jingmei

N1 - data source: no data used

PY - 2018

Y1 - 2018

N2 - 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.

AB - 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.

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