TY - JOUR
T1 - Spectral bounds for the connectivity of regular graphs with given order
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.
U2 - 10.13001/1081-3810.3675
DO - 10.13001/1081-3810.3675
M3 - Article
SN - 1537-9582
VL - 34
SP - 428
EP - 443
JO - Electronic Journal of Linear Algebra
JF - Electronic Journal of Linear Algebra
ER -