Note on the second eigenvalue of regular graphs

2023/11/13 by Balla, Igor, Räty, Eero, Sudakov, Benny +1 · 3 citations
#Combinatorics (math.CO) #FOS: Mathematics

paper · doi:10.48550/arxiv.2311.07629

Abstract

The goal of this expository note is to give a short, self-contained proof of nearly optimal lower bounds for the second largest eigenvalue of the adjacency matrix of regular graphs.

Cited by

• The non-existence of some Moore polygons and spectral Moore bounds
• From small eigenvalues to large cuts, and Chowla's cosine problem
• An Alon-Boppana--type bound for very dense graphs, with applications to max-cut

Related

• Improved lower bounds on the extrema of eigenvalues of graphs
• Eigenvalue bounds for some classes of matrices associated with graphs
• Maximizing the order of a regular graph of given valency and second eigenvalue
• On the first two eigenvalues of regular graphs
• The Generalized RS-theorem