2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/73136It is conjectured that the Laplacian spectrum of a graph is majorized by its conjugate degree sequence. In this paper, we prove that this majorization holds for a class of graphs including trees. We also show that a generalization of this conjecture to graphs with Dirichlet boundary conditions is equivalent to the original conjecture.9 pagesCombinatorics05C50text