# How to determine whether the pair of graphs is Graphs Isomorphic

If two graphs $G_i$ and $G_j$ are isomorphic, please provide a bijection from the vertex set of $G_i$ to $G_j$, if the two graphs are not isomorphic, please provide a structural difference graphs

As There is an answer how to find weather two graphs are isomorphism or not in this link

I was wondering in such cases like example above which none of the ways to to prove isomorphism work, Then how we can see which of them are isomorphism ? except using Wikipedia's example .

I knew That $G_1$ and $G_2$ are isomorphic, I was just wondering how to determine $G_1$ and $G_2$ are isomorphic and how we can prove $G_3$ is not isomorphic to $G_1$ or $G_2$?

• Just a correction: the link that you provide mentions ways to show non-isomorphism. They are not ways to prove isomorphism as you mention. – Paresh Dec 12 '12 at 16:06