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GFact | Cayley’s formula for Number of Labelled Trees

Consider below questions.

  1. How many spanning trees can be there in a complete graph with n vertices?
  2. How many labelled Trees (please note trees, not binary trees) can be there with n vertices?

The answer is same for both questions.



For n = 2, there is 1 tree.

For n = 3, there are 3 trees.



For n = 4, there are 16 trees


The formula states that for a positive integer n, the number of trees on n labeled vertices is nn-2

Source:
https://en.wikipedia.org/wiki/Cayley%27s_formula

Article Tags :
GFacts
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