Determine whether the graph below is isomorphic to Petersen graph.

Question

At left is a graph, $G$, and at right is the Petersen graph.

I think they're isomorphic. I would like to know if I'm correct and how I can start a proof.

Answer 1

No they are not isomorphic, since G has a loop with 4 vertices (C, J, G, D), and the Petersen graph has only loops of size 5. I drawed G in GeoGebra and moved the vertices around to get:

Answer 2

They aren't isomorphic, because the other graph has an obvious Hamiltonian cycle, but the Petersen graph is nonhamiltonian.