1. ## Isomorphic

Which of the following graphs (see attached) is not isomorphic to the others, and why?

All graphs have 5 nodes
All graphs have 6 arcs
All graphs have 2 nodes of degree 3 and 3 nodes of degree 2
No graph has parallel arcs
No graphs have a loop
All graphs have a cycle
No graph is complete

What other characteristics can I look for to prove that one of these 5 graphs is not isomorphic?

(Also sorry for the bad paintbrush skills)

2. Originally Posted by meditate
Which of the following graphs (see attached) is not isomorphic to the others, and why?

All graphs have 5 nodes
All graphs have 6 arcs
All graphs have 2 nodes of degree 3 and 3 nodes of degree 2
No graph has parallel arcs
No graphs have a loop
All graphs have a cycle
No graph is complete

What other characteristics can I look for to prove that one of these 5 graphs is not isomorphic?

(Also sorry for the bad paintbrush skills)
How about the degee of the shortest cycle (that is the number of nodes in the closed cycle with the fewest nodes).

RonL