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An isomorphism exists between two graphs G and H if:
1. Number of vertices of G = Number of vertices of H.
2. Number of edges of G = Number of edges of H.
Please note that the above two points do not guarantee isomorphism.
In addition, if f is a function obtained from a relationship between the vertices of G and the vertices of H, then f should be a one to one and onto function (bijection) and the number of vertices with same degree, must be same in G and H. A degree is the number of edges connected to a vertex.