2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/113840We give a necessary and sufficient condition for $k$-step nilmanifolds associated with graphs $(k \geq 3)$ to admit Anosov automorphisms. We also prove nonexistence of Anosov automorphisms on certain classes of 2-step and 3-step nilmanifolds.16 pagesDynamical SystemsDifferential Geometry37D20;22E25text