Thread: Isomorphism Proof

I'm having difficulty with this proof since I'm not sure how the two iffs affect the layout of the solution:

Show that two simple graphs and are isomorphic if and only if there is a bijection such that if and only if .

Any help would be much appreciated,
Ultros

It is considered impossible to prove a definition.
If the above is not given as the definition of isomorphic graphs, then how does your textbook define isomorphic graphs?

Two graphs G and H are said to be isomorphic if there are bijections and such that if and only if . Where is a graph's incidence function, e is an edge, and u and v are vertices.