  The fractional matching number of a graph G, is the maximum size of a
fractional matching of G. The following sharp lower bounds for a graph G of
order n are proved, and all extremal graphs are characterized in this paper.
(1)The sum of the fractional matching number of a graph G and the fractional
matching number of its complement is not less than n/2 , where n is not less
than 2. (2) If G and its complement are non-empty, then the sum of the
fractional matching number of a graph G and the fractional matching number of
its complement is not less than (n+1)/2, where n is not less than 28. (3) If G
and its complement have no isolated vertices, then the sum of the fractional
matching number of a graph G and the fractional matching number of its
complement is not less than (n+4)/2, where n is not less than 28.
