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and more rooted than unrooted trees. The last distinction is the most biologically relevant; it arises because there are many places on an unrooted tree to put the root. For bifurcating labeled trees, the total number of rooted trees is:

: for , represents the number of leaf nodes.

For bifurcating labeled trees, the total number of unrooted trees is:

: for .

Among labeled bifurcating trees, the number of unrooted trees with leaves is equal to the number of rooted trees with leaves.

The number of rooted

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