Is it true that two graphs must be Isomorphic if:
- They have 8 vertices, each with a degree of 3?
- They are both connected, without cycles, and have 6 edges?
So I know that to be Isomorphic, each graph must have the same number of vertices connected in the same way. So for for the first question, I would have to show that a vertex might have a degree of 3 on one graph but not connect to the same three vertices as another, or that it must... I am confused on how to show this.
And my understanding for the second question, is that two connected graphs without cycles are pretty much a tree (?). I am confused on how to show these are/aren't isomorphic as well.
Any help/hints are appreciated.