Abstract
This article has two main results. First, we develop a simple algorithm to list all nonisomorphic rooted plane trees in lexicographic order using a level sequence representation. Then, by selecting a unique centroid to act as the root of a free plane tree, we apply the rooted plane tree algorithm to develop an algorithm to list all nonisomorphic free plane trees. The latter algorithm also uses a level sequence representation and lists all free plane trees with a unique centroid first followed by all free plane trees with two centroids. Both algorithms are proved to run in constant amortized time using straightforward bounding methods.
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