2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/142877We study some new isoperimetric inequalities on graphs. We etablish a relation between the volume entropy (or asymptotic volume), the systole and the first Betti number of weighted graphs. We also find bounds for the volume, associated to some special measure, of the unit ball for the stable norm of graphs.Metric GeometryCombinatorics05C35, 37B10text