For n = 1, we need at least -1 edges. This seems troublesome, take some other value.
For n = 2, we need at least -1 edges. Again, take some other value.
For n = 3, we need at least 0 edges.
So, such graphs possible for 3 vertices are:-
$1 + 3 +3+1$ (for 0 edges, for 1 edge, for 2 edges and for 3 edges respectively) => $8$
Look at Option D. It is:
${^3C_0} + {^3C_1} + {^3C_2} + {^3C_3}$
=> $1 + 3 +3+1$ => $8$