2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/155992For $n \geq 2$ and a local field $K$, let $Δ_n$ denote the affine building naturally associated to the symplectic group ${\rm Sp}_n(K)$. We compute the spectral radius of the subgraph $Y_n$ of $Δ_n$ induced by the special vertices in $Δ_n$, from which it follows that $Y_n$ is an analogue of a family of expanders and is non-amenable.minor corrections made; 11 pages, 2 figures; to appear in Ars CombinatoriaCombinatorics05C12 (Primary), 05C25, 51E24 (Secondary)text