A Beautiful Graph Theory "Prüf"
Автор: Nice Math Problems
Загружено: 2023-09-26
Просмотров: 2679
Описание:
The number of trees on n labelled vertices is given by Cayley’s Formula n^(n − 2). But why?
This is where the Prüfer sequence comes in...
A Prüfer sequence is a clever way to encode any tree with n vertices into a sequence of length (n − 2), where each number can take any of the values from 1 to n. This video shows how to prove that the number of Prüfer sequences is equal to the number of labelled trees.
Image credits:
Neurons clip by Ahsan Ashraf, via Pixabay
Decision tree image by A.Gholamzade, CC BY-SA 4.0, via Wikimedia Commons
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