mayank0802's blog

Counting Trees??
By mayank0802, history, 6 years ago, In English

How many different trees can be formed with N nodes?? I read somewhere it is N ^ (N — 2), But doesn't find any proof? May anyone elaborate how it is N ^ (N — 2).

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6 years ago, # |
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http://www-math.mit.edu/~djk/18.310/18.310F04/counting_trees.html

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6 years ago, # |
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Is this formula is approximation??

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6 years ago, # |
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This problem solution "number of spanning trees in labeled complete graph is $$$n^{n-2}$$$", is called Cayley's Formula, which is famous in graph theory field.

There is a famous proof by Heinz Prüfer (1918) which uses Prüfer Code. But we can able to count number of spanning trees in any undirected simple graph $$$G$$$ via determinant of matrix. This way is called Kirchhoff's Theorem.

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