ohk,
sum of degree = 2 * edges
3 * 10 + 1 * 8 + 2 * 5 + x1 + x2 + x3 + x4 = 2 * 31
x1 + x2 + x3 + x4 = 62 - 48
x1 + x2 + x3 + x4 = 14
each node have degree atleast three means
x1 + x2 + x3 + x4 = 14 - 4 * 3 = 2
x1 + x2 + x3 + x4 = 2
Means either one node take 2 value , means one node have degree 3 + 2 : 5 ( Not possible , because their are only 2 nodes of degree 5 )
Or
two nodes have 1 , 1 value means two nodes have 4 degree , and left two nodes have 3 degree.
Hence nodes having degree = 3 are 2.