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A complete description of trees with maximal possible number of maximum independent sets among all n-vertex trees with exactly l leaves is obtained. For all values of the parameters n and l the extremal tree is unique and is the result of merging the endpoints of l simple paths. [ABSTRACT FROM AUTHOR]

For any n, in the set of n-vertex trees such that any two leaves have no common adjacent vertex, we describe the trees with the smallest number of maximal independent sets. [ABSTRACT FROM AUTHOR]