Question

1. How many non-isomorphic unrooted trees are there with five vertices?

2. How many non-isomorphic rooted trees are there with five vertices (using isomorphism for directed graphs)?

Short answer

1. 3
2. 9

Step-by-step solution

Definition

The tree which are not isomorphic are non-isomorphic trees.

Two trees \({T_1}\) and \({T_2}\) are said to be isomorphic if there is a one-to-one correspondence between edged of \({T_1}\) and \({T_2}\).

Check whether the trees are isomorphic or not

(a). Number of unrooted non-isomorphic trees with 5 vertices is 3

The trees are:

(b). Number of rooted non-isomorphic trees with 5 vertices is 9