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The AHU-algorithm solves the computationally difficult graph isomorphismproblem for rooted trees, and does so with a linear time complexity. Althoughthe AHU-algorithm has remained state of the art for almost 50 years, it hasbeen criticized for being unclearly presented, and no complete proof ofcorrectness has been given. In this text, that gap is filled: we formalize thealgorithm's main point of assigning and compressing labels to provide acharacterization of isomorphic rooted trees, and then proceed with proving thecorrectness and optimal runtime of the AHU-algorithm.

Isomorphism Testing of Rooted Trees in Linear Time