On eigenvalue multiplicity in signed graphs

Abstract

Given a signed graph Σ with n vertices, let μ be an eigenvalue of Σ, and let t be the codimension of the corresponding eigenspace. We prove that [Formula presented] whenever μ∉{0,1,−1}. 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.