Question: 1. Perhaps keeping pigeons in mind, show that if a simple graph has at least two vertices, then two of its vertices must have the same degree.
2. Draw a graph with degree sequence (1,1,2,2). Now draw one with degree sequence (1,1,1,1,1,1). Can you find more graphs with these degree sequences?
3. Think of at least two different proofs that Kn has (n(n - 1)/2) edges.