2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/61941We consider a sparse random subraph of the $n$-cube where each edge appears independently with small probability $p(n) =O(n^{-1+o(1)})$. In the most interesting regime when $p(n)$ is not exponentially small we prove that the largest eigenvalue of the graph is asymtotically equal to the square root of the maximum degree.CombinatoricsMathematical PhysicsProbabilitytext