Martínez Pérez, ÁlvaroRodríguez, José M.2026-04-102026-04-10202610.1007/s00025-026-02636-1https://hdl.handle.net/20.500.14352/1346412026 Acuerdos transformativos CRUEHerein we study the relationship on graphs between being (metric) doubling and these two properties: being p-parabolic and satisfying the Cheeger isoperimetric inequality. We prove that if a uniform graph G satisfies the (Cheeger) isoperimetric inequality, then G is not (metric) doubling and see that the converse is not true. We also prove that if G is a doubling graph with doubling constant C, then it is p-parabolic for every p ≥ log2(C) and see that the converse is not true. Furthermore, we see that being doubling does not imply being p-parabolic for every 1 <p< ∞. Finally, we see that a quasi-isometry between manifolds whose Ricci curvature is bounded below preserves being doubling and also, that an manifold with bounded Ricci curvature below is doubling if and only any uniform graph quasi-isometric to it is doubling.engAttribution 4.0 Internationalhttp://creativecommons.org/licenses/by/4.0/journal articlehttps://doi.org/10.1007/s00025-026-02636-1open accessDoublingIsoperimetric inequalityParabolicityp-parabolicityQuasi-isometriesCiencias12 Matemáticas