Find two graphs with the same score, but one is a tree and the other is not a tree

Question

The question is pretty self-explanatory: Find a tree and a non-tree which have the same graph score. (The score of the graph is a sequence of the degrees of the graph from smallest to the largest)

I am thinking about one thing:

A graph is a tree when it is cyclic and connected. So if I want to make a graph which is not a tree, I think I should use the acyclic property of the tree

Answer 1

Well, I found it. This is the second easiest solution. The tree is:

                  O-O-O-O-O-O 

with the score of $1,1,2,2,2,2$.

The non-tree is:

                     O-O-O 

                       O 
                      / \
                     O - O

for which the score is $1,1,2,2,2,2$.

The simplest is (thanks to Stinking Bishop):

Tree:

                    O-O-O-O-O

The other graph:

                       O-O

                        O
                       / \
                      O - O

Their score is $1,1,2,2,2$