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That is, the right child of a left child, or the left child of a right child. The best that I can come up with is the "opposing child" but I was wondering if anyone has come across an existing naming convention for this.

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    $\begingroup$ Minor comment on the form: I believe that, ideally, the question should stand on its own and not refer to the title $\endgroup$
    – integrator
    Jan 14, 2020 at 19:28
  • $\begingroup$ If you are interested in terms for a broader set of relationships, you might want to consider modifying kinship terms from anthropology. $\endgroup$
    – Mars
    Jan 15, 2020 at 4:01

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You can use 'sibling' (or 'brother'/'sister' if you prefer to gender the vertices). It's somewhat commonly used, but you may want to redefine it quickly when using it extensively.

NB: this terminology can be used for non-binary tree, the sibling of a vertex is any other vertex with the same parent/father.

While you may want to find a more reliable source, Wikipedia agrees with me at the moment: https://en.m.wikipedia.org/wiki/Tree_structure

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