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How many of the following sequences can be the degrees of the vertices of a con...

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How many of the following sequences can be the degrees of the vertices of a connected simple graph (on 5 vertices)?

  • 2, 1, 1, 1, 1
  • 2, 2, 2, 1, 1
  • 3, 3, 1, 1, 1
  • 4, 3, 2, 1, 0
  • 4, 4, 2, 1, 1

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