2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/61618We prove that for all values of the edge probability p(n) the largest eigenvalue of a random graph G(n,p) satisfies almost surely: λ_1(G)=(1+o(1))max{\sqrtΔ,np}, where Δis a maximal degree of G, and the o(1) term tends to zero as max{\sqrtΔ,np} tends to infinity.CombinatoricsProbability05C80 (Primary) 15A52, 60B** (Secondary)text