lets take graph with 3 vertices , v1,v2,v3 , now assign different degree to each vertices for d(v1)=0 , d(v2)=1 ,d(v3)=2 , now use handshaking theoram that is 2*edge=sum of degree of each vertices , which also conclude that sum of degrees of vertices should be even
now , add each degree of each vertices that is = 0+1+2 =3(which is not even) to make this even u have to make v3=1 , or v1=1,v2=1,v3=2 or v1=0,v2=0,v3=0 and so many possibilities
now if some people argue for v1=2,v2=3,v3=5 , for that we cant tale such example for 3 vertices graph because simple graph(no loop and parallel edges) is given