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I know that graph Isomorphism should be verified in polynomial time but I’m a little confused about how to approach the problem. Any directions would be greatly appreciated. How can i show that a graph Isomorphism is in NP.
You can show this by giving either a polynomial-time nondeterministic algorithm solving graph-isomorphism or by giving a polynomial time deterministic algorithm checking that a certificate for graph isomorphism is indeed a certificate for graph isomorphism.
Showing that there exists a polynomial-time deterministic certificate-checking algorithm should not be too complicated. A certificate for this problem would be a mapping of nodes from one graph to the nodes of the other graph. So you can then check if all edges are mapped over correctly as well, if the mapping of nodes is bijective, etc…