In directed Case : degrees possible 0,1,2
Let
I = nodes with degree 2
L = nodes with degree 0
X = nodes with degree 1
Sum of degrees = Number of edges [since directed]
I(2) + L(0) + X(1) = [I+L+X] - 1
2I + X = I + L + X -1
I = L - 1 ==> L = I +1
@Shaik Masthan
Please correct if wrong :(