Are these non isomorphic graphs?

Question

I have graph $A$:

I have graph $B$:

Are graph $A$ and $B$ non-isomorphic because?

I think yes, because:

• graph $A$ has $V_{8}$ with degree vertex $4$ and graph $B$ has $V_{8}$ with degree vertex $2$.

• or vertices $V_{8}, V_{1} $ in graph $A$ are neighboring, but in graph $B$ vertices $V_{8}, V_{1}$ are not neighboring.

Is that correct?

Answer 1

No, this is not correct. For example, your first bullet point only shows that $V_8$ in graph $A$ cannot correspond to $V_8$ in graph $B$. Why can't there be an isomorphism that takes $V_8$ in graph $A$ to some other vertex in graph $B$? (I am not saying there is -- I have not checked -- but your argument is not sufficient to prove that the graphs are non-isomorphic.)

Remember, the labels are not part of the graph and are just for convenience in identifying particular vertices.