2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/115329Let F(G) be a fixed linear combination of the k extremal eigenvalues of a graph G and of its complement. The problem of finding max{F(G):v(G)=n} generalizes a number of problems raised previously in the literature. We show that the limit max{F(G):v(G)=n}/n exists when n tends to infinity. We also answer a question of Gernert about the sum of the two maximal eigenvalues of a graph.Some calculation errors from the first version have been correctedCombinatoricsCommutative Algebra05C50text