Abstract
Ashoot is a fixed subset of branches rooted at a given vertex of a tree. We show that interchanging two nonintersecting shoots is an isomorphism of a tree only in two trivial cases: when either the shoots are isomorphic as rooted trees or their roots are similar in a tree obtained by deleting the shoots without the roots. The proof is based on a sufficient condition for similarity of two vertices in a tree. We also consider some applications of the above results to problems concerning Number Deck reconstruction of a tree.
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Krasikov, I. Interchanging branches and similarity in a tree. Graphs and Combinatorics 7, 165–175 (1991). https://doi.org/10.1007/BF01788141
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DOI: https://doi.org/10.1007/BF01788141