2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/64499We find the maximum number of maximal independent sets in two families of graphs: all graphs with $n$ vertices and at most $r$ cycles, and all such graphs that are also connected. In addition, we characterize the extremal graphs.31 pages, 11 figures, Latex, see related papers at http://www.math.msu.edu/~sagan, split paper into two partsCombinatorics05C35 (Primary) 05C69 (Secondary)text