Maximal Independent Sets In Graphs With At Most r Cycles

We 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.Comment: 31 pages, 11 figures, Latex, see related papers at http://www.math.msu.edu/~sagan, split paper into two part