ISOMORPHISM:
For isomorphism of any two graph ,it is necessary that the matrix representation of both of the graphs should be same . it means that when we erase the label of graph then both graph should be equal.
few theorems are there which says about isomorphism :
1. no of vertices of G1 and G2 should be same.
2.no of edges of G1 and G2 should be same.
3.degree sequence of G1 and G2 should be same .
4.no of cycles of one length in G1 and G2 should be same .
5.degree of neighboring vertex corresponding any other vertex in both of the graph should be same.
Above all theorems are sufficient to prove G1 and G2 are isomorphic to each other.
NOW , the question is about subset .subset incudes equal also . so when G1 and G2 are isomorpjhic to each other then we can say that G1 is also subset of G2. but it cant be the proper subset of G2.
proper subset is strict about atleast 1 less.
hope it will help you .
:)