Discrete Math 2

Assume there is a graph with an arbitrary edge "e" in a random graph of "G" with your desired number of edges. Prove that G-e (G with edge removed) is connected if and only if e is in a cycle of G.

7. Let G be a connected graph and e any edge in G. Prove that G - e (i.e. G with edge e removed) is connected if and only if e is in a cycle of G