G-Fact 20 (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


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