On the number of nonisomorphic subtrees of a tree

preprint2016arXivOpen access

We show that a tree of order $n$ has at most $O(5^{n/4})$ nonisomorphic subtrees, and that this bound is best possible. We also prove an analogous result for the number of nonisomorphic rooted subtrees of a rooted tree.

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On the number of nonisomorphic subtrees of a tree

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