The wikipedia article for 'isomorphism' states that βif two objects are isomorphic, then any property that is isomorphism conserves, and that applies to one of the objects, also applies to the other.
So your question should indicate if you care about form, data, performance, etc.
If you care about the behavior of the binary tree for the search, your algorithm is incorrect. See What does it mean to be isomorphic for two binary trees?
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