Trees in grapyh theor

[Rock]

Dears;

If we have 5 vertices, hwo many trees can we form with order 5? and in general if we have n vertices? hwo many trees the we can formed?

Regards

 

[pka]

If we have 5 vertices, hwo many trees can we form with order 5? and in general if we have n vertices? hwo many trees the we can formed?

Any tree \(\displaystyle \mathcal{T}\) is an connected acyclic graph.

A standard theorem states that a tree \(\displaystyle \mathcal{T}\) is connect and has \(\displaystyle n-1\) edges if it has \(\displaystyle n\) vertices.

In this case \(\displaystyle n=5\) so it should be a simple matter to draw and count.

Try to generalize.

 

[Rock]

Any tree \(\displaystyle \mathcal{T}\) is an connected acyclic graph.

A standard theorem states that a tree \(\displaystyle \mathcal{T}\) is connect and has \(\displaystyle n-1\) edges if it has \(\displaystyle n\) vertices.

In this case \(\displaystyle n=5\) so it should be a simple matter to draw and count.

Try to generalize.

what is the meaning of cycles and what is the relation betwwen trees and cycles?

thank you very much

 

[pka]

what is the meaning of cycles and what is the relation betwwen trees and cycles?

That is the whole point: trees are acyclic graphs.
There are no cycles.