  For a fixed graph G, a maximal independent set is an independent set that is
not a proper subset of any other independent set. P. Erd\"os, and
independently, J. W. Moon and L. Moser, and R. E. Miller and D. E. Muller,
determined the maximum number of maximal independent sets in a graph on n
vertices, as well as the extremal graphs. In this paper we maximize the number
of maximal independent sets of a fixed size for all graphs of order n and
determine the extremal graphs. Our result generalizes the classical result.
