A generalization of Fiedler's lemma and its applications

In this article, taking a Fiedler's result on the spectrum of a matrix formed from two symmetric matrices as a motivation, we deduce a more general result on the eigenvalues of a matrix, which form from n symmetric matrices. As an important application, we obtain the adjacency spectra, Laplacian spectra and signless Laplacian spectra of a graph with a particular almost equitable partition. (c) 2024 Elsevier Inc. All rights are reserved, including those for text and data mining, AI training, and similar technologies.