Trees with maximum number of maximal matchings

Forests on n vertices with maximum number of maximal matchings are called extremal   forests. All extremal forests, except 2K12K1, are trees. Extremal trees with small number n   of vertices, n⩽19n⩽19, are characterized; in particular, they are unique if n≠6n≠6. The exponential upper and lower bounds on the maximum number of maximal matchings among n-vertex trees have been found.