Question: If every vertex in a directed graph G has positive out-degree (at least one outwardly directed edge), then must G contain a directed circuit? Explain

If every vertex in a directed graph G has positive out-degree

If every vertex in a directed graph G has positive out-degree (at least one outwardly directed edge), then must G contain a directed circuit? Explain why or give a counter-example. Show that if an n-vertex graph has more than n-1)(n - 2) edges, then it must be connected. (Hint: the most edges possible in a disconnecteed graph will occur when there are two components, each complete subgraphs.)

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