On eigenvalue multiplicity in signed graphs

TL;DR

This paper establishes a cubic polynomial upper bound on the eigenvalue multiplicity in signed graphs, demonstrates its sharpness with examples, and explores cases where the bound can be lowered.

Contribution

It introduces a new cubic polynomial bound on eigenvalue multiplicity in signed graphs and shows its optimality with explicit examples.

Findings

Bound is sharp, attained by specific signed graphs

Eigenvalue multiplicity is limited by a cubic polynomial

Certain cases allow for a reduced bound

Abstract

For signed graphs we provide a cubic polynomial upper bound on the multiplicity of its eigenvalues. We show that this bound is sharp by providing examples of signed graphs in which it is attained. We also discuss particular cases in which the bound can be decreased.