Graph isomorphism of two graphs

Question

Today was my exam of discrete structure.

In one question we needed to find whether graphs are isomorphic or not..

Vertices, edges, and degree sequence are same

But in the Graph of G there is the cycle length of 5 aefcba. But in the second graph there is no cycle with the length of 5. According to me they are not isomorphic...

But in my class it is only me who is saying that graphs are not isomorphic...

Am I wrong?

Sorry for my bad english: p

Answer 1

You are correct, but your proof is missing the part where you prove that there is no cycle of length 5 in the second graph.

An easy proof is to show that the second graph is bipartite, while the first graph is not... which also completes your proof, because a bipartite graph cannot have an odd-length cycle.