Basic Examples (1) 

The Prüfer code of a labeled tree:

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Properties and Relations (6) 

Use FromDigits to obtain an integer-valued Prüfer code:

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For a tree with n vertices, the length of the Prüfer code is n-2:

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Empty Prüfer code corresponds to a tree with only two leaves:

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The resource function PruferCodeToLabeledTree can be used to reconstruct the tree from its Prüfer code:

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The Prüfer code of a path is a sequence of n-2 distinct integers:

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The Prüfer code for an n-pointed star with the center vertex k is a sequence of n-1 copies of k:

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Possible Issues (2) 

LabeledTreeToPruferCode does not work on non-explicit trees:

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Substitute numbers for symbolic values to find the Prüfer code:

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LabeledTreeToPruferCode accepts only trees with vertices numbered sequentially, starting from 1:

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Normalize labeling:

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