. For each of the following sequences, find out if there is any simple graph on 5 or 6 verticessuch that the degrees of its vertices are given by that sequence.

If you claim that there isno such graph, provide an argument supporting this claim, otherwise draw a graph with thecorresponding degree sequence.

5 vertices 6 vertices

(a) 5; 3; 2; 2; 2 (d) 5; 5; 3; 2; 2; 1

(b) 3; 3; 3; 3; 2 (e) 5; 1; 1; 1; 1; 1

(c) 3; 3; 3; 2; 2 ( f) 3; 3; 3; 3; 0; 0

My answers :

(a) 5+3+2+2+2 = 14/5 = 2 and 4/5 (d) 5+5+3+2+2+1 = 18/6 =3

(b) 3+3+3+3+2 = 14/5 = 2 and 4/5 (e) 5+1+1+1+1+1 = 10/2 = 5

(c) 3+3+3+2+2 = 13/5 = 2 and 3/5 (f) 3+3+3+3+0+0 = 12/6 = 2

Am I right in saying that (a) ,(b) , (c) ,(d) ,(e) are not simple graphs as they have odd edges after they are summed and divided ? and f can be a simple graph as its edges are even.

If i am missing something please let me know

thanks