Equiangular lines and eigenvalue multiplicities

TL;DR

This paper explores the mathematical problem of finding the maximum number of equiangular lines with a fixed angle and examines the related issue of second eigenvalue multiplicity in graphs, providing insights into their interconnection.

Contribution

It offers an expository analysis of the relationship between equiangular lines and eigenvalue multiplicities, highlighting new perspectives on these classical problems.

Findings

Clarifies the connection between equiangular lines and eigenvalue multiplicities.

Provides bounds and conditions for maximum equiangular lines.

Discusses implications for graph eigenvalue problems.

Abstract

Expository article on the problem of determining the maximum number of equiangular lines with a fixed angle, and the associated problem of second eigenvalue multiplicity in graphs.