Suppose G is a simple, nonconnected graph with n vertices that is maximal with respect to these properties. That is, if you tried to make a larger graph in which G is a subgraph, this larger graph will lose at least one of the properties (a) simple, (b) nonconnected, or (c) has n vertices.
What does being maximal with respect to these properties imply about G?G? That is, what further properties must GG possess because of this assumption?
In this activity you hopefully decided that a graph as described in the activity must:
Prove these two statements.
Hint: For each of the two proofs, you might consider arguing by contrapositive or by contradiction.
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