We find the maximum number of maximal independent sets in two families of graphs. The first family consists of all graphs with n vertices and at most r cycles. The second family is all graphs of the first family which are connected and satisfy n 3r. Partially supported by an award from DIMACS and an NSF VIGRE grant to the Rutgers University Department of Mathematics. 1
Goh Chee Ying, Koh Khee Meng, Bruce E. Sagan, Vinc