@article{beyer,
author = {Beyer, Terry and Hedetniemi, Sandra Mitchell},
title = {Constant Time Generation of Rooted Trees},
journal = {SIAM Journal on Computing},
volume = {9},
number = {4},
pages = {706-712},
year = {1980},
doi = {10.1137/0209055},
URL = {https://doi.org/10.1137/0209055},
eprint = {https://doi.org/10.1137/0209055},
abstract = { This paper generalizes a result of Ruskey [SIAM J. Comput., 7(1978), pp. 424–439] for generating k-ary trees lexicographically to generating all rooted trees with n vertices. An algorithm is presented which generates canonical representations of these trees in a well-defined order. As in other works, the average number of steps per tree is constant. }
}