Spectral Bounds for the Connectivity of Regular Graphs with Given Order

Main Article Content

Aida Abiad
Boris Brimkov
Xavier Martinez-Rivera
Suil O
Jingmei Zhang


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.

Article Details


Most read articles by the same author(s)