The nullity of a graph is the multiplicity of the eigenvalue zero in its spectrum. Among n-vertex trees, the star has greatest nullity (equal to n - 2). We generalize this by showing that among n-vertex trees whose vertex degrees do not exceed a certain value D, the greatest nullity is n - 2⌈(n - 1)/D⌉. Methods for constructing such maximum-nullity trees are described. © 2004 Elsevier Inc. All rights reserved.
Fiorini, S., Gutman, I., & Sciriha, I. (2005). Trees with maximum nullity. Linear Algebra and Its Applications, 397(1–3), 245–251. https://doi.org/10.1016/j.laa.2004.10.024