I have three graphs illustrated above and my goal is to identify if they are isomorphic or not. For disprove that they are isomorphic, I could point out properties such as having a cycle of a certain length or by the neighborhood of one particular vertex, but I can´t find a property to distinguish the two last ones. Any suggestions?
EDIT: I could find an isomorphism between the first and the second graph with the relabeling from the first to the second one: $0 \to 0; 1 \to 4; 2 \to 3; 4 \to 2; 8 \to 1; 3 \to 5; 6 \to 8; 5 \to 6; 7 \to 7; 9 \to 9$
As you can see from the illustration, in the second graph you can start from any vertex and find a 5 lines long road to go itself again. Whichs in the third one you can’t. So the third one is not isomorphic to the first and second one, which are isomorphical as you mentioned in your EDIT.