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 nn-2
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