Graphs and Hermitian matrices: Exact interlacing
We prove conditions for equality between the extreme eigenvalues of a matrix and its quotient. In particular, we give a lower bound on the largest singular value of a matrix and generalize a result of Finck and Grohmann about the largest eigenvalue of a graph. © 2007 Elsevier B.V. All rights reserved.
Bollobás, B., & Nikiforov, V. (2008). Graphs and Hermitian matrices: Exact interlacing. Discrete Mathematics, 308 (20), 4816-4821. https://doi.org/10.1016/j.disc.2007.08.076