2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/159042We investigate the structure of trees that have greatest maximum eigenvalue among all trees with a given degree sequence. We show that in such an extremal tree the degree sequence is non-increasing with respect to an ordering of the vertices that is obtained by breadth-first search. This structure is uniquely determined up to isomorphism. We also show that the maximum eigenvalue in such classes of trees is strictly monotone with respect to majorization.9 pages, 2 figuresCombinatorics05C35; 05C75; 05C05; 05C50text