2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/115645We find a sharp bound for the order of the automorphism group of a stable curve of genus $g$ with $3g-3$ nodes, and a sharp bound for the order of the automorphism group of such a curve with all smooth components. Combined with the results of our article math.CO/0608645 we find that graph theoretically, the cubic graph with a given number of vertices and most automorphisms is simple, but algebro-geometrically, the stable curves with $3g-3$ nodes that have the most automorphisms have non-simple dual graph.14 pagesAlgebraic GeometryCombinatorics14H37, 05Ctext