Explain why there can't be a simple graph with the following sequence of vertex degrees: (a) 5,1,1,1

(b) 4,3,3,1,1,1,1,1

a cant exist because 3 out of the 4 vertices must have only one degree vertex and the remaining one must have 5.

b) This example can be a single graph because of the handshaking lemma. The sum of the odd degrees vertex must be an even number: 3+3+5=11