G-Fact 20 (Cayley’s formula for Number of Labelled Trees)

Consider below questions.

- How many spanning trees can be there in a complete graph with n vertices?
- 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 **n ^{n-2}**

**Source: **

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

This article is contributed by **Vaibhav Gupta**. Please write comments if you find anything incorrect, or you want to share more information about the topic discussed above