Eigenvalue multiplicity in quartic graphs

Citation

Capaverde J & Rowlinson P (2017) Eigenvalue multiplicity in quartic graphs. Linear Algebra and Its Applications, 535, pp. 160-170. https://doi.org/10.1016/j.laa.2017.08.023

Abstract
Let G be a connected quartic graph of order n with μ as an eigenvalue of multiplicity k. We show that if μ ∉ {−1,0} then k ≤ (2n − 5)/3 when n ≤ 22, and k ≤ (3n − 1)/5 when n ≥ 23. If μ ∈ {−1,0} then k ≤ (2n + 2)/3, with equality if and only if G = K5 (with μ = −1) or G = K4,4 (with μ = 0).

Keywords
Eigenvalue; Quartic graph; Star complement

Journal
Linear Algebra and Its Applications: Volume 535