On eigenvalue multiplicity in signed graphs

Citation

Ramezani F, Rowlinson P & Stanić Z (2020) On eigenvalue multiplicity in signed graphs. Discrete Mathematics, 343 (10), Art. No.: 111982. https://doi.org/10.1016/j.disc.2020.111982

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 n ≤ t+2/3 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.

Keywords
Signed graph; Eigenvalue multiplicity; Net-regular signed graph; Star complement

Journal
Discrete Mathematics: Volume 343, Issue 10